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Author ID: jentzen.arnulf Recent zbMATH articles by "Jentzen, Arnulf"
Published as: Jentzen, Arnulf; Jentzen, A.
Homepage: http://www.ajentzen.de/
External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr
Awards: Felix Klein Prize (2020)
all top 5

Co-Authors

3 single-authored
31 Hutzenthaler, Martin
16 Kloeden, Peter Eris
14 Beck, Christian
13 Becker, Sebastian
13 Riekert, Adrian
12 Cheridito, Patrick
11 Kruse, Thomas
10 Kuckuck, Benno
10 von Wurstemberger, Philippe
9 Kurniawan, Ryan
9 Salimova, Diyora F.
9 Welti, Timo
8 Grohs, Philipp
7 E, Weinan
7 Lindner, Felix
7 Pušnik, Primož
5 Gonon, Lukas
5 Rossmannek, Florian
4 Cox, Sonja Gisela
4 Hefter, Mario
4 Hornung, Fabian
4 Neufeld, Ariel David
3 Andersson, Adam
3 Gess, Benjamin
3 Han, Jiequn
3 Ibragimov, Shokhrukh
3 Kröger, Timo
3 Müller-Gronbach, Thomas
3 Neuenkirch, Andreas
3 Nguyen, Tuan-Anh
3 Röckner, Michael
3 Yaroslavtseva, Larisa
2 Beneventano, Pierfrancesco
2 Eberle, Simon
2 Graeber, Robin
2 Jacobe de Naurois, Ladislas
2 Mazzonetto, Sara
2 Padgett, Joshua Lee
2 Weiss, Georg Sebastian
1 Ackermann, Julia
1 Beccari, Matteo
1 Bercher, Aritz
1 Berger, Arno
1 Berner, Julius
1 Blömker, Dirk
1 Boussange, Victor
1 Braunwarth, Ramon
1 Caraballo Garrido, Tomás
1 Conus, Daniel
1 Da Prato, Giuseppe
1 Dereich, Steffen
1 Elbrächter, Dennis
1 Fehrman, Benjamin J.
1 Gallon, Davide
1 Gerencsér, Máté
1 Giles, Michael B.
1 Hairer, Martin
1 Han, Xiaoying
1 Hudde, Anselm
1 Jaafari, Nor
1 Kassing, Sebastian
1 Kleinberg, Konrad
1 Kofler, David
1 Koppensteiner, Sarah
1 Leber, Frank
1 Magnani, Emilia
1 Müller, Marvin S.
1 Noll, Marco
1 Pellissier, Loïc
1 Pohl, Katharina
1 Scarpa, Luca
1 Schneisgen, Daniela
1 Schwab, Christoph
1 Shen, Hao
1 Siegmund, Stefan
1 Šiška, David
1 Stadtmüller, Uli
1 Stelzer, Robert
1 Tuan Anh Nguyen
1 van Neerven, Jan M. A. M.
1 Wang, Xiaojie
1 Winkel, Georg
1 Zimmermann, Philipp
all top 5

Serials

7 Discrete and Continuous Dynamical Systems. Series B
5 Journal of Mathematical Analysis and Applications
4 IMA Journal of Numerical Analysis
4 Journal of Complexity
4 The Annals of Applied Probability
4 Foundations of Computational Mathematics
3 The Annals of Probability
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 SIAM Journal on Numerical Analysis
3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
3 Communications in Mathematical Sciences
3 SN Partial Differential Equations and Applications
2 BIT
2 Memoirs of the American Mathematical Society
2 Journal of Scientific Computing
2 Journal of Nonlinear Science
2 Potential Analysis
2 Journal of Machine Learning Research (JMLR)
2 Journal of Numerical Mathematics
2 Stochastic and Partial Differential Equations. Analysis and Computations
2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Bulletin of the Australian Mathematical Society
1 Nonlinearity
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Mathematics of Computation
1 Applied Mathematics and Computation
1 Applied Mathematics and Optimization
1 IEEE Transactions on Automatic Control
1 Journal of Computational and Applied Mathematics
1 Journal of Differential Equations
1 Numerische Mathematik
1 Transactions of the American Mathematical Society
1 Constructive Approximation
1 European Journal of Applied Mathematics
1 Numerical Algorithms
1 Proceedings of the National Academy of Sciences of the United States of America
1 Stochastic Processes and their Applications
1 SIAM Journal on Scientific Computing
1 Advances in Computational Mathematics
1 Electronic Journal of Probability
1 Finance and Stochastics
1 Mathematical Finance
1 Infinite Dimensional Analysis, Quantum Probability and Related Topics
1 Communications in Nonlinear Science and Numerical Simulation
1 Stochastics and Dynamics
1 Milan Journal of Mathematics
1 CBMS-NSF Regional Conference Series in Applied Mathematics
1 Communications in Computational Physics
1 Communications in Mathematics and Statistics
1 SIAM Journal on Mathematics of Data Science

Publications by Year

Citations contained in zbMATH Open

86 Publications have been cited 2,968 times in 1,344 Documents Cited by Year
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
390
2018
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016
E, Weinan; Han, Jiequn; Jentzen, Arnulf
244
2017
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
226
2011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
202
2012
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1330.60084
Hutzenthaler, Martin; Jentzen, Arnulf
114
2015
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116
Beck, Christian; E, Weinan; Jentzen, Arnulf
106
2019
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011
Jentzen, Arnulf; Kloeden, Peter E.
78
2009
Taylor approximations for stochastic partial differential equations. Zbl 1240.35001
Jentzen, Arnulf; Kloeden, Peter
74
2011
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
64
2019
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
60
2020
Deep optimal stopping. Zbl 1495.60029
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf
59
2019
The numerical approximation of stochastic partial differential equations. Zbl 1205.60130
Jentzen, A.; Kloeden, P. E.
59
2009
Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Zbl 1480.60191
Berner, Julius; Grohs, Philipp; Jentzen, Arnulf
52
2020
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Zbl 07206753
Hutzenthaler, Martin; Jentzen, Arnulf
51
2020
Galerkin approximations for the stochastic Burgers equation. Zbl 1267.60071
Blömker, Dirk; Jentzen, Arnulf
47
2013
Loss of regularity for Kolmogorov equations. Zbl 1322.35083
Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
44
2015
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Zbl 1241.60030
Jentzen, Arnulf; Röckner, Michael
41
2012
Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Zbl 1176.60051
Jentzen, Arnulf
40
2009
Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
39
2009
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Zbl 1472.65157
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh; von Wurstemberger, Philippe
39
2020
Solving the Kolmogorov PDE by means of deep learning. Zbl 1490.65006
Beck, Christian; Becker, Sebastian; Grohs, Philipp; Jaafari, Nor; Jentzen, Arnulf
38
2021
A Milstein scheme for SPDEs. Zbl 1318.60072
Jentzen, Arnulf; Röckner, Michael
36
2015
Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
36
2011
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
35
2013
Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202
Jentzen, Arnulf; Kloeden, Peter
35
2010
A mild Itô formula for SPDEs. Zbl 1423.35472
Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael
32
2019
Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. Zbl 1475.65157
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
32
2021
DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 1500.35009
Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph
32
2022
Deep splitting method for parabolic PDEs. Zbl 1501.65054
Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel
31
2021
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Zbl 1490.60202
E, Weinan; Han, Jiequn; Jentzen, Arnulf
31
2022
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Zbl 1432.65011
Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie
26
2018
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Zbl 1253.65006
Hutzenthaler, Martin; Jentzen, Arnulf
26
2011
A random Euler scheme for Carathéodory differential equations. Zbl 1160.65003
Jentzen, A.; Neuenkirch, A.
25
2009
Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. Zbl 1403.60052
Becker, Sebastian; Jentzen, Arnulf
24
2019
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Zbl 1469.60220
Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
24
2020
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. Zbl 1477.65020
Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan
23
2019
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
22
2021
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161
Jentzen, Arnulf; Pušnik, Primož
21
2020
On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Zbl 1355.65012
Jentzen, Arnulf; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa
19
2016
Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015
Kloeden, Peter E.; Jentzen, Arnulf
19
2007
Higher order pathwise numerical approximations of SPDEs with additive noise. Zbl 1228.65015
Jentzen, Arnulf
19
2011
Solving high-dimensional optimal stopping problems using deep learning. Zbl 1505.91413
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Welti, Timo
19
2021
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. Zbl 1471.65169
Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
17
2020
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Zbl 07679303
Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; von Wurstemberger, Philippe
16
2023
Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305
Jentzen, Arnulf; Kloeden, Peter E.
14
2009
Convergence rates for the stochastic gradient descent method for non-convex objective functions. Zbl 1520.68143
Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf
13
2020
Taylor expansions of solutions of stochastic partial differential equations. Zbl 1201.60064
Jentzen, Arnulf
13
2010
Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Zbl 1406.60102
Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora
12
2019
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094
E, Weinan; Jentzen, Arnulf; Shen, Hao
12
2016
An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068
Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E.
12
2016
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Zbl 1473.65251
Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
12
2020
Uniform error estimates for artificial neural network approximations for heat equations. Zbl 1502.65171
Gonon, Lukas; Grohs, Philipp; Jentzen, Arnulf; Kofler, David; Šiška, David
12
2022
Exponential moments for numerical approximations of stochastic partial differential equations. Zbl 1416.60072
Jentzen, Arnulf; Pušnik, Primož
11
2018
Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. Zbl 1490.65232
Grohs, Philipp; Jentzen, Arnulf; Salimova, Diyora
11
2022
On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Zbl 1425.91401
Hefter, Mario; Jentzen, Arnulf
10
2019
Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. Zbl 1403.60059
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
10
2019
Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. Zbl 1517.60081
Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E.
10
2023
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054
Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo
10
2021
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities. Zbl 1501.65084
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
10
2022
Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations. Zbl 1405.60094
Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo
9
2018
An overview on deep learning-based approximation methods for partial differential equations. Zbl 07675828
Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf; Kuckuck, Benno
9
2023
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143
Jentzen, Arnulf; Kurniawan, Ryan
9
2021
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Zbl 1473.35670
Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan
9
2021
On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations. Zbl 1490.60200
Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf
9
2021
Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. Zbl 1433.68353
Jentzen, Arnulf; von Wurstemberger, Philippe
8
2020
Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071
Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe
8
2021
Non-convergence of stochastic gradient descent in the training of deep neural networks. Zbl 1494.65044
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian
7
2021
On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Zbl 1373.34092
Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan; Welti, Timo
7
2017
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces. Zbl 1431.60051
Andersson, Adam; Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan
5
2019
On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Zbl 1404.60082
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora
5
2017
An improved maximum allowable transfer interval for \(L^p\)-stability of networked control systems. Zbl 1368.93642
Jentzen, Arnulf; Leber, Frank; Schneisgen, Daniela; Berger, Arno; Siegmund, Stefan
5
2010
Full error analysis for the training of deep neural networks. Zbl 1492.65132
Beck, Christian; Jentzen, Arnulf; Kuckuck, Benno
5
2022
On the mild Itô formula in Banach spaces. Zbl 1402.60067
Cox, Sonja; Jentzen, Arnulf; Kurniawan, Ryan; Pušnik, Primož
4
2018
On existence and uniqueness properties for solutions of stochastic fixed point equations. Zbl 1462.60096
Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf
4
2021
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. Zbl 1502.65037
Cheridito, Patrick; Jentzen, Arnulf; Riekert, Adrian; Rossmannek, Florian
4
2022
Space-time error estimates for deep neural network approximations for differential equations. Zbl 07649348
Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; Zimmermann, Philipp
4
2023
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Zbl 1472.60111
Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E.
3
2020
Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. Zbl 1485.60061
Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo
3
2021
Pathwise convergence of numerical schemes for random and stochastic differential equations. Zbl 1179.65009
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2
2009
On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values. Zbl 1471.34116
Jentzen, Arnulf; Kuckuck, Benno; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa
2
2021
Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions. Zbl 1491.68179
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian
2
2022
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. Zbl 1515.65025
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Tuan Anh Nguyen
2
2023
Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality. Zbl 07693253
Grohs, Philipp; Ibragimov, Shokhrukh; Jentzen, Arnulf; Koppensteiner, Sarah
1
2023
A unified existence and uniqueness theorem for stochastic evolution equations. Zbl 1200.60051
Jentzen, A.; Kloeden, P. E.
1
2010
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions. Zbl 07575573
Jentzen, Arnulf; Riekert, Adrian
1
2022
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation. Zbl 07595126
Jentzen, Arnulf; Riekert, Adrian
1
2023
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Zbl 07679303
Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; von Wurstemberger, Philippe
16
2023
Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. Zbl 1517.60081
Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E.
10
2023
An overview on deep learning-based approximation methods for partial differential equations. Zbl 07675828
Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf; Kuckuck, Benno
9
2023
Space-time error estimates for deep neural network approximations for differential equations. Zbl 07649348
Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; Zimmermann, Philipp
4
2023
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. Zbl 1515.65025
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Tuan Anh Nguyen
2
2023
Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality. Zbl 07693253
Grohs, Philipp; Ibragimov, Shokhrukh; Jentzen, Arnulf; Koppensteiner, Sarah
1
2023
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation. Zbl 07595126
Jentzen, Arnulf; Riekert, Adrian
1
2023
DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 1500.35009
Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph
32
2022
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Zbl 1490.60202
E, Weinan; Han, Jiequn; Jentzen, Arnulf
31
2022
Uniform error estimates for artificial neural network approximations for heat equations. Zbl 1502.65171
Gonon, Lukas; Grohs, Philipp; Jentzen, Arnulf; Kofler, David; Šiška, David
12
2022
Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. Zbl 1490.65232
Grohs, Philipp; Jentzen, Arnulf; Salimova, Diyora
11
2022
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities. Zbl 1501.65084
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
10
2022
Full error analysis for the training of deep neural networks. Zbl 1492.65132
Beck, Christian; Jentzen, Arnulf; Kuckuck, Benno
5
2022
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. Zbl 1502.65037
Cheridito, Patrick; Jentzen, Arnulf; Riekert, Adrian; Rossmannek, Florian
4
2022
Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions. Zbl 1491.68179
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian
2
2022
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions. Zbl 07575573
Jentzen, Arnulf; Riekert, Adrian
1
2022
Solving the Kolmogorov PDE by means of deep learning. Zbl 1490.65006
Beck, Christian; Becker, Sebastian; Grohs, Philipp; Jaafari, Nor; Jentzen, Arnulf
38
2021
Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. Zbl 1475.65157
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
32
2021
Deep splitting method for parabolic PDEs. Zbl 1501.65054
Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel
31
2021
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
22
2021
Solving high-dimensional optimal stopping problems using deep learning. Zbl 1505.91413
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Welti, Timo
19
2021
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054
Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo
10
2021
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143
Jentzen, Arnulf; Kurniawan, Ryan
9
2021
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Zbl 1473.35670
Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan
9
2021
On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations. Zbl 1490.60200
Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf
9
2021
Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071
Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe
8
2021
Non-convergence of stochastic gradient descent in the training of deep neural networks. Zbl 1494.65044
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian
7
2021
On existence and uniqueness properties for solutions of stochastic fixed point equations. Zbl 1462.60096
Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf
4
2021
Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. Zbl 1485.60061
Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo
3
2021
On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values. Zbl 1471.34116
Jentzen, Arnulf; Kuckuck, Benno; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa
2
2021
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
60
2020
Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Zbl 1480.60191
Berner, Julius; Grohs, Philipp; Jentzen, Arnulf
52
2020
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Zbl 07206753
Hutzenthaler, Martin; Jentzen, Arnulf
51
2020
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Zbl 1472.65157
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh; von Wurstemberger, Philippe
39
2020
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Zbl 1469.60220
Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
24
2020
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161
Jentzen, Arnulf; Pušnik, Primož
21
2020
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. Zbl 1471.65169
Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
17
2020
Convergence rates for the stochastic gradient descent method for non-convex objective functions. Zbl 1520.68143
Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf
13
2020
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Zbl 1473.65251
Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
12
2020
Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. Zbl 1433.68353
Jentzen, Arnulf; von Wurstemberger, Philippe
8
2020
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Zbl 1472.60111
Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E.
3
2020
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116
Beck, Christian; E, Weinan; Jentzen, Arnulf
106
2019
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
64
2019
Deep optimal stopping. Zbl 1495.60029
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf
59
2019
A mild Itô formula for SPDEs. Zbl 1423.35472
Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael
32
2019
Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. Zbl 1403.60052
Becker, Sebastian; Jentzen, Arnulf
24
2019
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. Zbl 1477.65020
Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan
23
2019
Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Zbl 1406.60102
Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora
12
2019
On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Zbl 1425.91401
Hefter, Mario; Jentzen, Arnulf
10
2019
Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. Zbl 1403.60059
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
10
2019
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces. Zbl 1431.60051
Andersson, Adam; Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan
5
2019
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
390
2018
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Zbl 1432.65011
Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie
26
2018
Exponential moments for numerical approximations of stochastic partial differential equations. Zbl 1416.60072
Jentzen, Arnulf; Pušnik, Primož
11
2018
Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations. Zbl 1405.60094
Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo
9
2018
On the mild Itô formula in Banach spaces. Zbl 1402.60067
Cox, Sonja; Jentzen, Arnulf; Kurniawan, Ryan; Pušnik, Primož
4
2018
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016
E, Weinan; Han, Jiequn; Jentzen, Arnulf
244
2017
On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Zbl 1373.34092
Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan; Welti, Timo
7
2017
On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Zbl 1404.60082
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora
5
2017
On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Zbl 1355.65012
Jentzen, Arnulf; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa
19
2016
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094
E, Weinan; Jentzen, Arnulf; Shen, Hao
12
2016
An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068
Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E.
12
2016
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1330.60084
Hutzenthaler, Martin; Jentzen, Arnulf
114
2015
Loss of regularity for Kolmogorov equations. Zbl 1322.35083
Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
44
2015
A Milstein scheme for SPDEs. Zbl 1318.60072
Jentzen, Arnulf; Röckner, Michael
36
2015
Galerkin approximations for the stochastic Burgers equation. Zbl 1267.60071
Blömker, Dirk; Jentzen, Arnulf
47
2013
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
35
2013
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
202
2012
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Zbl 1241.60030
Jentzen, Arnulf; Röckner, Michael
41
2012
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
226
2011
Taylor approximations for stochastic partial differential equations. Zbl 1240.35001
Jentzen, Arnulf; Kloeden, Peter
74
2011
Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
36
2011
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Zbl 1253.65006
Hutzenthaler, Martin; Jentzen, Arnulf
26
2011
Higher order pathwise numerical approximations of SPDEs with additive noise. Zbl 1228.65015
Jentzen, Arnulf
19
2011
Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202
Jentzen, Arnulf; Kloeden, Peter
35
2010
Taylor expansions of solutions of stochastic partial differential equations. Zbl 1201.60064
Jentzen, Arnulf
13
2010
An improved maximum allowable transfer interval for \(L^p\)-stability of networked control systems. Zbl 1368.93642
Jentzen, Arnulf; Leber, Frank; Schneisgen, Daniela; Berger, Arno; Siegmund, Stefan
5
2010
A unified existence and uniqueness theorem for stochastic evolution equations. Zbl 1200.60051
Jentzen, A.; Kloeden, P. E.
1
2010
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011
Jentzen, Arnulf; Kloeden, Peter E.
78
2009
The numerical approximation of stochastic partial differential equations. Zbl 1205.60130
Jentzen, A.; Kloeden, P. E.
59
2009
Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Zbl 1176.60051
Jentzen, Arnulf
40
2009
Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
39
2009
A random Euler scheme for Carathéodory differential equations. Zbl 1160.65003
Jentzen, A.; Neuenkirch, A.
25
2009
Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305
Jentzen, Arnulf; Kloeden, Peter E.
14
2009
Pathwise convergence of numerical schemes for random and stochastic differential equations. Zbl 1179.65009
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2
2009
Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015
Kloeden, Peter E.; Jentzen, Arnulf
19
2007
all top 5

Cited by 1,963 Authors

66 Jentzen, Arnulf
27 Mao, Xuerong
26 Hutzenthaler, Martin
24 Kloeden, Peter Eris
24 Wang, Xiaojie
16 Liu, Wei
15 E, Weinan
15 Gan, Siqing
15 Hong, Jialin
13 Karniadakis, George Em
13 Reisinger, Christoph
13 Schwab, Christoph
12 Kovács, Mihály
12 Kruse, Thomas
12 Larsson, Stig
12 Tambue, Antoine
11 Lang, Annika
11 Liu, Mingzhu
11 Przybyłowicz, Paweł
11 Song, Minghui
11 Szpruch, Lukasz
10 Becker, Sebastian
10 Han, Jiequn
10 Hu, Junhao
10 Kruse, Raphael
10 Lord, Gabriel James
10 Mishra, Siddhartha
10 Ngo, Hoang-Long
10 Petersen, Philipp Christian
10 Redmann, Martin
10 Sabanis, Sotirios
10 Ying, Lexing
10 Yuan, Chenggui
9 Andersson, Adam
9 Beck, Christian
9 Bréhier, Charles-Edouard
9 Cui, Jianbo
9 Grohs, Philipp
9 Guo, Qian
9 Kumar, Chaman
9 Lu, Jianfeng
9 Warin, Xavier
9 Yang, Haizhao
8 Cao, Yanzhao
8 Gao, Shuaibin
8 Li, Xiaoyue
8 Neuenkirch, Andreas
8 Qi, Ruisheng
8 Yan, Zhenya
8 Yang, Hongfu
8 Zhang, Qimin
8 Zhao, Weidong
7 Blömker, Dirk
7 Kamrani, Minoo
7 Kuznetsov, Dmitriĭ Feliksovich
7 Liu, Zhihui
7 Mukam, Jean Daniel
7 Perdikaris, Paris G.
7 Wu, Fuke
6 Bayer, Christian
6 Cheridito, Patrick
6 Duan, Jinqiao
6 Fan, Yuwei
6 Jiao, Yuling
6 Kutyniok, Gitta
6 Lindner, Felix
6 Mirzaee, Farshid
6 Müller-Gronbach, Thomas
6 Nguyen, Tuan-Anh
6 Oosterlee, Cornelis Willebrordus
6 Petersson, Andreas
6 Schneider, Reinhold
6 Šiška, David
6 Taguchi, Dai
6 Yaroslavtseva, Larisa
6 Zhang, Wei
5 Asai, Yusuke
5 Bachouch, Achref
5 Bao, Feng
5 Cao, Wanrong
5 Darbon, Jerome
5 Dareiotis, Konstantinos Anastasios
5 Del Moral, Pierre
5 dos Reis, Gonçalo
5 Gerencsér, Máté
5 Gonon, Lukas
5 Gu, Yiqi
5 Han, Xiaoying
5 Hu, Ruimeng
5 Huang, Chengming
5 Huang, Jianguo
5 Kühn, Christian
5 Kurniawan, Ryan
5 Li, Yangrong
5 Lu, Xiliang
5 Luong, Duc-Trong
5 Nguwi, Jiang Yu
5 Oh, Tadahiro
5 Pham, Huyên
5 Privault, Nicolas
...and 1,863 more Authors
all top 5

Cited in 245 Serials

100 Journal of Computational Physics
76 Journal of Computational and Applied Mathematics
42 Computer Methods in Applied Mechanics and Engineering
42 Applied Mathematics and Computation
39 SIAM Journal on Numerical Analysis
39 Journal of Scientific Computing
31 Applied Numerical Mathematics
31 SIAM Journal on Scientific Computing
31 Communications in Computational Physics
27 Stochastic and Partial Differential Equations. Analysis and Computations
25 Journal of Mathematical Analysis and Applications
24 Discrete and Continuous Dynamical Systems. Series B
23 BIT
22 The Annals of Applied Probability
21 Stochastic Processes and their Applications
18 Numerical Algorithms
18 International Journal of Computer Mathematics
17 Computers & Mathematics with Applications
16 Communications in Nonlinear Science and Numerical Simulation
16 SIAM Journal on Financial Mathematics
14 Mathematics of Computation
14 Stochastic Analysis and Applications
13 Quantitative Finance
12 Journal of Complexity
12 Advances in Computational Mathematics
11 Multiscale Modeling & Simulation
10 Journal of Differential Equations
10 Monte Carlo Methods and Applications
10 Electronic Journal of Probability
10 SN Partial Differential Equations and Applications
9 Mathematics and Computers in Simulation
9 Numerische Mathematik
9 Stochastics and Dynamics
9 Analysis and Applications (Singapore)
8 SIAM Journal on Control and Optimization
8 Physica D
8 Foundations of Computational Mathematics
8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
7 Mathematical Methods in the Applied Sciences
7 Chaos, Solitons and Fractals
7 Applied Mathematics and Optimization
7 Calcolo
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 Computational and Applied Mathematics
7 Applied Mathematical Finance
7 Mathematical Finance
7 Methodology and Computing in Applied Probability
7 Differentsial’nye Uravneniya i Protsessy Upravleniya
7 Advances in Difference Equations
7 East Asian Journal on Applied Mathematics
7 Research in the Mathematical Sciences
6 Journal of Computational Mathematics
6 Discrete and Continuous Dynamical Systems. Series S
6 Numerical Mathematics: Theory, Methods and Applications
6 Communications in Theoretical Physics
5 Statistics & Probability Letters
5 Computational Mechanics
5 European Journal of Applied Mathematics
5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
5 Engineering Analysis with Boundary Elements
5 Finance and Stochastics
5 Abstract and Applied Analysis
5 Communications in Mathematics and Statistics
5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
5 SIAM Journal on Mathematics of Data Science
4 Inverse Problems
4 Journal of the Franklin Institute
4 Memoirs of the American Mathematical Society
4 Systems & Control Letters
4 Constructive Approximation
4 MCSS. Mathematics of Control, Signals, and Systems
4 Neural Networks
4 Japan Journal of Industrial and Applied Mathematics
4 Journal of Nonlinear Science
4 SIAM Journal on Applied Dynamical Systems
4 International Journal of Numerical Analysis and Modeling
4 Mathematical Biosciences and Engineering
4 Oberwolfach Reports
4 Advances in Applied Mathematics and Mechanics
4 Journal of Computational Dynamics
4 SIAM/ASA Journal on Uncertainty Quantification
3 Journal of Statistical Physics
3 Nonlinearity
3 Physics Letters. A
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 The Annals of Probability
3 Journal of Optimization Theory and Applications
3 Chinese Annals of Mathematics. Series B
3 Journal of Theoretical Probability
3 SIAM Review
3 Potential Analysis
3 Discrete and Continuous Dynamical Systems
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 Nonlinear Dynamics
3 Vietnam Journal of Mathematics
3 Infinite Dimensional Analysis, Quantum Probability and Related Topics
3 Journal of Evolution Equations
3 Computational Methods in Applied Mathematics
3 Journal of Numerical Mathematics
3 Journal of Applied Mathematics and Computing
...and 145 more Serials
all top 5

Cited in 43 Fields

919 Numerical analysis (65-XX)
757 Probability theory and stochastic processes (60-XX)
383 Partial differential equations (35-XX)
363 Computer science (68-XX)
127 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
116 Ordinary differential equations (34-XX)
103 Systems theory; control (93-XX)
67 Biology and other natural sciences (92-XX)
65 Fluid mechanics (76-XX)
64 Calculus of variations and optimal control; optimization (49-XX)
58 Statistics (62-XX)
53 Approximations and expansions (41-XX)
52 Dynamical systems and ergodic theory (37-XX)
40 Operations research, mathematical programming (90-XX)
36 Statistical mechanics, structure of matter (82-XX)
30 Mechanics of deformable solids (74-XX)
25 Integral equations (45-XX)
23 Operator theory (47-XX)
21 Functional analysis (46-XX)
17 Quantum theory (81-XX)
11 Linear and multilinear algebra; matrix theory (15-XX)
11 Harmonic analysis on Euclidean spaces (42-XX)
10 Real functions (26-XX)
6 Special functions (33-XX)
6 Classical thermodynamics, heat transfer (80-XX)
5 General and overarching topics; collections (00-XX)
5 Difference and functional equations (39-XX)
5 Geophysics (86-XX)
5 Information and communication theory, circuits (94-XX)
4 Optics, electromagnetic theory (78-XX)
3 Global analysis, analysis on manifolds (58-XX)
2 Number theory (11-XX)
2 Functions of a complex variable (30-XX)
2 Integral transforms, operational calculus (44-XX)
2 Astronomy and astrophysics (85-XX)
1 History and biography (01-XX)
1 Mathematical logic and foundations (03-XX)
1 Commutative algebra (13-XX)
1 Category theory; homological algebra (18-XX)
1 Measure and integration (28-XX)
1 Convex and discrete geometry (52-XX)
1 General topology (54-XX)
1 Mechanics of particles and systems (70-XX)

Citations by Year

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