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Krylov, Nicolaĭ Vladimirovich

Author ID: krylov.nicolai-v Recent zbMATH articles by "Krylov, Nicolaĭ Vladimirovich"
Published as: Krylov, N. V.; Krylov, Nicolai V.; Krylov, Nicolai; Krylov, N.; Krylov, Nicolaï
Further Spellings: Крылов Николай Владимирович
Homepage: http://www.math.umn.edu/~nkrylov/
External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef
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Serials

16 Theory of Probability and its Applications
16 Mathematics of the USSR. Izvestiya
14 Probability Theory and Related Fields
14 Mathematics of the USSR, Sbornik
13 Matematicheskiĭ Sbornik. Novaya Seriya
13 Communications in Partial Differential Equations
13 SIAM Journal on Mathematical Analysis
12 Stochastic Processes and their Applications
10 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
9 The Annals of Probability
9 Applied Mathematics and Optimization
8 Teoriya Veroyatnosteĭ i eë Primeneniya
8 St. Petersburg Mathematical Journal
7 Soviet Mathematics. Doklady
6 Journal of Functional Analysis
6 Journal of Mathematical Sciences (New York)
6 Stochastic and Partial Differential Equations. Analysis and Computations
5 Potential Analysis
5 Methods and Applications of Analysis
4 Mathematics of Computation
4 Siberian Mathematical Journal
4 Sibirskiĭ Matematicheskiĭ Zhurnal
4 Transactions of the American Mathematical Society
4 Electronic Journal of Probability
3 Lithuanian Mathematical Journal
3 Uspekhi Matematicheskikh Nauk [N. S.]
3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
3 Stochastics and Stochastics Reports
3 Graduate Studies in Mathematics
2 Mathematical Notes
2 Russian Mathematical Surveys
2 Stochastics
2 Ukrainian Mathematical Journal
2 Ukraïns’kyĭ Matematychnyĭ Zhurnal
2 Differentsial’nye Uravneniya
2 Differential Equations
2 Illinois Journal of Mathematics
2 Journal of Soviet Mathematics
2 Proceedings of the American Mathematical Society
2 Differential and Integral Equations
2 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika
2 Journal of Dynamics and Differential Equations
2 Topological Methods in Nonlinear Analysis
2 Calculus of Variations and Partial Differential Equations
2 NoDEA. Nonlinear Differential Equations and Applications
2 Doklady Mathematics
2 Mathematical Surveys and Monographs
2 Applications of Mathematics
1 Applicable Analysis
1 Archive for Rational Mechanics and Analysis
1 Matematicheskie Zametki
1 Moscow University Mathematics Bulletin
1 Collectanea Mathematica
1 Transactions of the Moscow Mathematical Society
1 Trudy Moskovskogo Matematicheskogo Obshchestva
1 Selecta Mathematica Sovietica
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Litovskiĭ Matematicheskiĭ Sbornik
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Izvestiya Rossiĭskoĭ Akademii Nauk. Seriya Matematicheskaya
1 Russian Academy of Sciences. Izvestiya. Mathematics
1 Trudy Seminara Imeni I. G. Petrovskogo
1 Electronic Journal of Differential Equations (EJDE)
1 Ulam Quarterly
1 Journal of Convex Analysis
1 Statistical Inference for Stochastic Processes
1 Communications in Contemporary Mathematics
1 Theory of Stochastic Processes
1 Discrete and Continuous Dynamical Systems. Series B
1 Communications on Pure and Applied Analysis
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Stochastics
1 Journal of Mathematical Physics, Analysis, Geometry
1 Complex Variables and Elliptic Equations
1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya
1 Lecture Notes in Mathematics
1 Mathematics and Its Applications. Soviet Series
1 Translations of Mathematical Monographs
1 Student Mathematical Library
1 Analysis and Mathematical Physics
1 Mathematics in Engineering

Publications by Year

Citations contained in zbMATH Open

291 Publications have been cited 6,713 times in 4,030 Documents Cited by Year
Controlled diffusion processes. Transl. by A. B. Aries. Zbl 0459.93002
Krylov, N. V.
306
1980
Lectures on elliptic and parabolic equations in Hölder spaces. Zbl 0865.35001
Krylov, N. V.
290
1996
Nonlinear elliptic and parabolic equations of the second order. Transl. from the Russian by P. L. Buzytsky. Zbl 0619.35004
Krylov, N. V.
276
1987
Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001
Krylov, N. V.
253
2008
Strong solutions of stochastic equations with singular time dependent drift. Zbl 1072.60050
Krylov, N. V.; Röckner, M.
238
2005
Existence of strong solutions for Itô’s stochastic equations via approximations. Zbl 0847.60038
Gyöngy, István; Krylov, Nicolai
237
1996
Fokker-Planck-Kolmogorov equations. Zbl 1342.35002
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V.
184
2015
Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079
Krylov, N. V.
176
2007
An analytic approach to SPDEs. Zbl 0933.60073
Krylov, N. V.
171
1999
Stochastic evolution equations. Zbl 0462.60060
Krylov, N. V.; Rozovskij, B. L.
161
1981
On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions. Zbl 0997.35012
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
138
2001
Eine gewisse Eigenschaft der Lösungen parabolischer Gleichungen mit meßbaren Koeffizienten. Zbl 0439.35023
Krylov, N. V.; Safonov, M. V.
131
1980
Bounded inhomogeneous elliptic and parabolic equations. Zbl 0511.35002
Krylov, N. V.
124
1982
Some new results in the theory of controlled diffusion processes. Zbl 0436.93055
Krylov, N. V.
119
1980
A certain property of solutions of parabolic equations with measurable coefficients. Zbl 0464.35035
Krylov, N. V.; Safonov, M. V.
114
1981
Nonlinear elliptic and parabolic equations of second order. (Нелинейные ѐллиптические и параболические уравнения второго порядка.) Zbl 0586.35002
Krylov, N. V.
80
1985
On the rate of convergence of finite-difference approximations for Bellman’s equations with variable coefficients. Zbl 0971.65081
Krylov, N. V.
80
2000
Controlled processes of diffusion type. (Управляемые процессы диффузионного типа.) Zbl 0513.60043
Krylov, N. V.
79
1977
Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others. Zbl 1138.35308
Kim, Doyoon; Krylov, N. V.
77
2007
Introduction to the theory of diffusion processes. Transl. from the Russian by V. Khidekel a. G. Pasechnik. Zbl 0844.60050
Krylov, N. V.
74
1995
Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052
Krylov, N. V.
72
2007
On stochastic equations with respect to semimartingales I. Zbl 0439.60061
Gyöngy, I.; Krylov, N. V.
70
1980
On stochastics equations with respect to semimartingales. II. Ito formula in Banach spaces. Zbl 0481.60060
Gyoengy, I.; Krylov, N. V.
69
1982
On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes. Zbl 0295.60057
Krylov, N. V.
68
1974
An estimate of the probability that a diffusion process hits a set of positive measure. Zbl 0459.60067
Krylov, N. V.; Safonov, M. V.
67
1979
Elliptic and parabolic equations for measures. Zbl 1194.35481
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
64
2009
On \(L_ p\)-theory of stochastic partial differential equations in the whole space. Zbl 0846.60061
Krylov, N. V.
62
1996
Parabolic equations with measurable coefficients. Zbl 1124.35024
Kim, Doyoon; Krylov, N. V.
59
2007
On the general notion of fully nonlinear second-order elliptic equations. Zbl 0832.35042
Krylov, N. V.
58
1995
Boundedly nonhomogeneous elliptic and parabolic equations. Zbl 0529.35026
Krylov, N. V.
57
1983
Controlled diffusion processes. Translated by A. B. Aries. Reprint of the 1980 ed. Zbl 1171.93004
Krylov, N. V.
54
2009
On the Cauchy problem for linear stochastic partial differential equations. Zbl 0396.60058
Krylov, N. V.; Rozovskii, B. L.
54
1977
A \(W_ 2^ n\)-theory of the Dirichlet problem for SPDEs in general smooth domains. Zbl 0794.60062
Krylov, N. V.
53
1994
Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Zbl 0578.35024
Krylov, N. V.
53
1984
On the splitting-up method and stochastic partial differential equations. Zbl 1028.60058
Gyöngy, István; Krylov, Nicolai
52
2003
Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation. Zbl 0362.35038
Krylov, N. V.
52
1976
Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352
Krylov, N. V.
51
2009
On the Itô–Wentzell formula for distribution-valued processes and related topics. Zbl 1238.60060
Krylov, N. V.
47
2011
A Sobolev space theory of SPDEs with constant coefficients in a half space. Zbl 0943.60047
Krylov, N. V.; Lototsky, S. V.
46
1999
Stochastic evolution equations. Zbl 1130.60069
Krylov, Nicolai V.; Rozovskii, Boris L.
42
2007
Weighted Sobolev spaces and Laplace’s equation and the heat equations in a half space. Zbl 0934.35032
Krylov, N. V.
42
1999
Itô’s formula for the \(L _{p }\)-norm of stochastic \({W^{1}_{p}}\)-valued processes. Zbl 1232.60050
Krylov, N. V.
41
2010
Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160
Krylov, N. V.; Priola, E.
41
2010
Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. Zbl 0980.60091
Krylov, N. V.
40
2001
On the Sobolev space theory of parabolic and elliptic equations in \(C^{1}\) domains. Zbl 1083.35041
Kim, Kyeong-Hun; Krylov, N. V.
40
2004
The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients. Zbl 1087.65100
Krylov, Nicolai V.
40
2005
The heat equation in \(L_{q}((0,T),L_{p})\)-spaces with weights. Zbl 0979.35060
Krylov, N. V.
37
2001
On Ito’s stochastic integral equations. Zbl 0281.60066
Krylov, N. V.
36
1969
A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204
Krylov, N. V.
35
2013
On Kolmogorov’s equations for finite dimensional diffusions. Zbl 0943.60070
Krylov, N. V.
35
1999
Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies. Zbl 1044.93546
Krylov, N. V.
33
1999
Control of a solution of a stochastic integral equation. Zbl 0265.60055
Krylov, N. V.
32
1972
Introduction to the theory of random processes. Zbl 1008.60001
Krylov, N. V.
32
2002
On weak uniqueness for some diffusions with discontinuous coefficients. Zbl 1073.60064
Krylov, N. V.
31
2004
On the rate of convergence of splitting-up approximations for SPDEs. Zbl 1038.60057
Gyöngy, István; Krylov, Nicolai
28
2003
A Sobolev space theory of SPDE with constant coefficients on a half line. Zbl 0928.60042
Krylov, N. V.; Lototsky, S. V.
28
1999
Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. Zbl 1401.35001
Krylov, N. V.
27
2018
On the rate of convergence of finite-difference approximations for Bellman’s equations. Zbl 0902.65035
Krylov, N. V.
26
1997
A simple proof of the existence of a solution of Itô’s equation with monotone coefficients. Zbl 0735.60061
Krylov, N. V.
26
1990
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211
Dong, Hongjie; Krylov, N. V.
26
2019
A generalization of the Littlewood-Paley inequality and some other results related to stochastic partial differential equations. Zbl 0870.42005
Krylov, N. V.
25
1994
The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains. Zbl 1127.65068
Dong, Hongjie; Krylov, Nicolai V.
24
2007
Elliptic regularity and essential self-adjointness of Dirichlet operators on \(\mathbb{R}^n\). Zbl 0901.35017
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael
24
1997
On the existence of \(W^2_p\) solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172
Krylov, N. V.
23
2013
An inequality in the theory of stochastic integrals. Zbl 0238.60038
Krylov, N. V.
22
1971
Regularity of invariant measures: The case of non-constant diffusion part. Zbl 0929.60039
Bogachev, V. I.; Krylov, N.; Röckner, M.
20
1996
On averaging principle for diffusion processes with null-recurrent fast component. Zbl 1053.60060
Khasminskii, R.; Krylov, N.
20
2001
On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
20
2013
On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale. Zbl 0625.35041
Krylov, N. V.
20
1987
On diffusion processes with drift in \(L_d\). Zbl 1480.60239
Krylov, N. V.
20
2021
Über stochastische Evolutionsgleichungen. Zbl 0436.60047
Krylov, N. V.; Rozovskij, B. L.
19
1979
On degenerate nonlinear elliptic equations. Zbl 0525.35038
Krylov, N. V.
19
1983
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094
Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai
19
2015
Maximum principle for SPDEs and its applications. Zbl 1135.60039
Krylov, Nicolai V.
18
2007
Stochastic partial differential equations and diffusion processes. Zbl 0518.60072
Krylov, N. V.; Rozovskij, B. L.
18
1982
Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009
Gyöngy, István; Krylov, Nicolai
18
2010
On time inhomogeneous stochastic Itô equations with drift in \(L_{D+1}\). Zbl 1483.60083
Krylov, N. V.
18
2021
Elliptic equations for measures: regularity and global bounds of densities. Zbl 1206.35242
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael
17
2006
Characteristics of degenerate second-order parabolic Ito equations. Zbl 0584.60068
Krylov, N. V.; Rozovskij, B. L.
17
1986
SPDEs in \(L_q(\mskip-2mu(0,\tau], L_p)\) spaces. Zbl 0963.60053
Krylov, N. V.
17
2000
On stochastic equations with drift in \({L_d}\). Zbl 1489.60102
Krylov, N. V.
17
2021
On conditional distributions of diffusion processes. Zbl 0402.60077
Krylov, N. V.; Rozovskii, B. L.
17
1978
Second-order elliptic and parabolic equations with \(B(\mathbb R^2, \mathrm{VMO})\) coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
16
2010
Fully nonlinear second order elliptic equations: recent development. Zbl 1033.35036
Krylov, Nicolai V.
16
1997
On the Calderón-Zygmund theorem with applications to parabolic equations. Zbl 1011.35033
Krylov, N. V.
16
2002
On characteristics of the degenerate second order Ito parabolic equations. Zbl 0503.60066
Krylov, N. V.; Rozovskij, B. L.
15
1982
On strong solutions of stochastic differential equations. Zbl 0481.60062
Zvonkin, A. K.; Krylov, N. V.
15
1975
Some properties of weighted Sobolev spaces in \(\mathbb{R}_+^d\). Zbl 0962.46016
Krylov, Nicolai V.
15
1999
On the foundation of the \(L_p\)-theory of stochastic partial differential equations. Zbl 1165.60331
Krylov, Nicolai V.
15
2006
Folgen konvexer Funktionen und Abschätzungen des Maximums der Lösung einer parabolischen Gleichung. Zbl 0354.35052
Krylov, N. V.
15
1976
On Shige Peng’s central limit theorem. Zbl 1433.60013
Krylov, N. V.
15
2020
On the first integrals and Liouville equations for diffusion processes. Zbl 0474.60049
Krylov, N. V.; Rozovskii, B. L.
14
1981
Parabolic equations in \(L_p\)-spaces with mixed norms. Zbl 1032.35046
Krylov, N. V.
14
2003
Smoothness of the value function for a controlled diffusion process in a domain. Zbl 0701.93054
Krylov, N. V.
13
1990
Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with \(C^1\) and \(C^2\) coefficients. Zbl 1085.65087
Dong, Hongjie; Krylov, Nicolai V.
13
2005
An accelerated splitting-up method for parabolic equations. Zbl 1101.35038
Gyöngy, István; Krylov, Nicolai
13
2005
On explicit formulas for solutions of stochastic equations. Zbl 0376.60067
Veretennikov, A. Yu.; Krylov, N. V.
13
1978
Some \(L_{p}\)-estimates for elliptic and parabolic operators with measurable coefficients. Zbl 1258.35069
Krylov, N. V.
13
2012
Über das Cauchyproblem für lineare stochastische partielle Differentialgleichungen. Zbl 0371.60076
Krylov, N. V.; Rozovskii, B. L.
13
1977
On estimates for the derivatives of solutions of nonlinear parabolic equations. Zbl 0598.35057
Krylov, N. V.
13
1984
On weak and strong solutions of time inhomogeneous Itô’s equations with VMO diffusion and Morrey drift. Zbl 07963483
Krylov, N. V.
1
2025
On parabolic equations in Morrey spaces with VMO \(a\) and Morrey \(b\), \(c\). Zbl 07974587
Krylov, N. V.
1
2025
On parabolic Adams’s, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces. Zbl 1542.35215
Krylov, Nicolai
7
2023
On potentials of Itô’s processes with drift in \(L_{d+1}\). Zbl 1533.60090
Krylov, N. V.
4
2023
Elliptic equations in Sobolev spaces with Morrey drift and the zeroth-order coefficients. Zbl 1522.35184
Krylov, N. V.
3
2023
On diffusion processes with drift in \(L_{d+1}\). Zbl 1543.60067
Krylov, N. V.
2
2023
On nondegenerate Itô processes with moderated drift. Zbl 1524.60112
Krylov, N. V.
2
2023
On diffusion processes with drift in a Morrey class containing \(L_{d+2}\). Zbl 1543.60068
Krylov, N. V.
2
2023
On strong solutions of Itô’s equations with \(D \sigma\) and \(b\) in Morrey classes containing \(L_d\). Zbl 07793390
Krylov, N. V.
2
2023
Estimates in \(L_p\) for solutions of SPDEs with coefficients in Morrey classes. Zbl 1534.60085
Krylov, N. V.
1
2023
On the heat equation with drift in \(L_{d+1}\). Zbl 1510.35090
Krylov, N. V.
4
2022
Linear and fully nonlinear elliptic equations with Morrey drift. Zbl 1511.35103
Krylov, N. V.
3
2022
Some properties of solutions of Itô equations with drift in \(L_{d+1}\). Zbl 1494.60065
Krylov, N. V.
3
2022
Aleksandrov’s estimates for elliptic equations with drift in Morrey spaces containing \(L_d\). Zbl 1482.35057
Dong, Hongjie; Krylov, N. V.
3
2022
Existence of strong solutions for Itô’s stochastic equations via approximations: revisited. Zbl 1499.60187
Gyöngy, I.; Krylov, N. V.
3
2022
On diffusion processes with drift in \(L_d\). Zbl 1480.60239
Krylov, N. V.
20
2021
On time inhomogeneous stochastic Itô equations with drift in \(L_{D+1}\). Zbl 1483.60083
Krylov, N. V.
18
2021
On stochastic equations with drift in \({L_d}\). Zbl 1489.60102
Krylov, N. V.
17
2021
On strong solutions of Itô’s equations with \(\sigma\in W_{\mathtt{d}}^1\) and \(\mathtt{b}\in{L_{\mathtt{d}}}\). Zbl 1497.60076
Krylov, N. V.
12
2021
Elliptic equations with VMO \(a,b\in L_d\), and \(c\in L_{d/2}\). Zbl 1460.35069
Krylov, N. V.
11
2021
Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey. Zbl 1468.35110
Krylov, N. V.
7
2021
On stochastic Itô processes with drift in \(L_d\). Zbl 1469.60186
Krylov, N. V.
5
2021
A review of some new results in the theory of linear elliptic equations with drift in \(L_d\). Zbl 1461.35002
Krylov, N. V.
2
2021
On Shige Peng’s central limit theorem. Zbl 1433.60013
Krylov, N. V.
15
2020
Linear and fully nonlinear elliptic equations with \(L_d\)-drift. Zbl 1460.35141
Krylov, Nicolai V.
11
2020
Weighted Aleksandrov estimates: PDE and stochastic versions. Zbl 1437.35206
Krylov, N. V.
1
2020
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211
Dong, Hongjie; Krylov, N. V.
26
2019
All functions are locally s-harmonic up to a small error. Zbl 1447.35358
Krylov, N. V.
4
2019
A few comments on a result of A. Novikov and Girsanov’s theorem. Zbl 1492.60113
Krylov, N. V.
3
2019
Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. Zbl 1401.35001
Krylov, N. V.
27
2018
\(C^{1+\alpha}\)-regularity of viscosity solutions of general nonlinear parabolic equations. Zbl 1402.35061
Krylov, N. V.
6
2018
On the existence of \(W_p^{1, 2}\) solutions for fully nonlinear parabolic equations under either relaxed or no convexity assumptions. Zbl 1405.35083
Krylov, N. V.
4
2018
Uniqueness for \(L_{p}\)-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms. Zbl 1394.35231
Krylov, N. V.
3
2018
On the existence of \(W_p^2\) solutions for fully nonlinear elliptic equations under either relaxed or no convexity assumptions. Zbl 1376.35049
Krylov, N. V.
11
2017
Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations. Zbl 1375.35551
Krylov, N. V.; Priola, Enrico
6
2017
On nonequivalence of regular boundary points for second-order elliptic operators. Zbl 1379.35099
Krylov, N. V.; Yastrzhembskiy, Timur
1
2017
Hörmander’s theorem for stochastic partial differential equations. Zbl 1439.60061
Krylov, N. V.
7
2016
On parabolic equations in one space dimension. Zbl 1346.35081
Krylov, N. V.
6
2016
Fokker-Planck-Kolmogorov equations. Zbl 1342.35002
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V.
184
2015
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094
Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai
19
2015
On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains. Zbl 1331.65122
Krylov, N. V.
11
2015
To the theory of viscosity solutions for uniformly parabolic Isaacs equations. Zbl 1329.35170
Krylov, N. V.
3
2015
Hypoellipticity for filtering problems of partially observable diffusion processes. Zbl 1317.60098
Krylov, N. V.
3
2015
Approximating the value functions for stochastic differential games with the ones having bounded second derivatives. Zbl 1302.49053
Krylov, N. V.
1
2015
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations. Zbl 1290.91022
Krylov, N. V.
10
2014
On \(C^{1+\alpha}\) regularity of solutions of Isaacs parabolic equations with VMO coefficients. Zbl 1304.35173
Krylov, N. V.
8
2014
On the rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman’s equations. Zbl 1297.65073
Krylov, N. V.
7
2014
Hörmander’s theorem for parabolic equations with coefficients measurable in the time variable. Zbl 1288.35315
Krylov, N. V.
6
2014
On regularity properties and approximations of value functions for stochastic differential games in domains. Zbl 1336.91020
Krylov, N. V.
5
2014
To the theory of viscosity solutions for uniformly elliptic Isaacs equations. Zbl 1302.35171
Krylov, N. V.
3
2014
On the independence of the value function for stochastic differential games of the probability space. Zbl 1307.91033
Krylov, N. V.
2
2014
On the fundamental matrix solution for higher-order parabolic systems. Zbl 1319.35075
Boccia, S.; Krylov, N. V.
1
2014
A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204
Krylov, N. V.
35
2013
On the existence of \(W^2_p\) solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172
Krylov, N. V.
23
2013
On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
20
2013
On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions. Zbl 1479.35526
Dong, Hongjie; Krylov, N. V.
9
2013
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains. Zbl 1287.49027
Krylov, N. V.
5
2013
An ersatz existence theorem for fully nonlinear parabolic equations without convexity assumptions. Zbl 1295.35262
Krylov, N. V.
4
2013
Interior estimates for second-order differences of solutions of finite-difference elliptic Bellman’s equations. Zbl 1269.49050
Krylov, N. V.
1
2013
Some \(L_{p}\)-estimates for elliptic and parabolic operators with measurable coefficients. Zbl 1258.35069
Krylov, N. V.
13
2012
On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions. Zbl 1285.35033
Krylov, Nicolai V.
11
2012
Interior estimates for the first-order differences for finite-difference approximations for elliptic Bellman’s equations. Zbl 1244.49053
Krylov, N. V.
2
2012
On the Itô–Wentzell formula for distribution-valued processes and related topics. Zbl 1238.60060
Krylov, N. V.
47
2011
On a representation of fully nonlinear elliptic operators in terms of pure second order derivatives and its applications. Zbl 1290.35099
Krylov, N. V.
10
2011
Filtering equations for partially observable diffusion processes with Lipschitz continuous coefficients. Zbl 1223.93112
Krylov, N. V.
6
2011
Filtering partially observable diffusions up to the exit time from a domain. Zbl 1233.62168
Krylov, N. V.; Wang, Teng
5
2011
Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space. Zbl 1223.65068
Gyöngy, István; Krylov, Nicolai
5
2011
Accelerated numerical schemes for PDEs and SPDEs. Zbl 1221.65222
Gyöngy, István; Krylov, Nicolai
2
2011
On divergence form second-order PDEs with growing coefficients in \(W^{1}_{p}\) spaces without weights. Zbl 1254.35108
Krylov, N. V.
1
2011
Itô’s formula for the \(L _{p }\)-norm of stochastic \({W^{1}_{p}}\)-valued processes. Zbl 1232.60050
Krylov, N. V.
41
2010
Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160
Krylov, N. V.; Priola, E.
41
2010
Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009
Gyöngy, István; Krylov, Nicolai
18
2010
Second-order elliptic and parabolic equations with \(B(\mathbb R^2, \mathrm{VMO})\) coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
16
2010
On Bellman’s equations with VMO coefficients. Zbl 1208.35052
Krylov, Nicolai V.
12
2010
About an example of N. N, Ural’tseva and weak uniqueness for elliptic operators. Zbl 1387.35149
Krylov, N. V.
3
2010
On divergence form SPDEs with growing coefficients in \(W^{1}_{2}\) spaces without weights. Zbl 1218.60057
Krylov, N. V.
3
2010
Kalman-Bucy filter and SPDEs with growing lower-order coefficients in \(W_{p}^{1}\) spaces without weights. Zbl 1260.60122
Krylov, N. V.
1
2010
Elliptic and parabolic equations for measures. Zbl 1194.35481
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
64
2009
Controlled diffusion processes. Translated by A. B. Aries. Reprint of the 1980 ed. Zbl 1171.93004
Krylov, N. V.
54
2009
Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352
Krylov, N. V.
51
2009
On divergence form SPDEs with VMO coefficients. Zbl 1195.60091
Krylov, N. V.
9
2009
On divergence form SPDEs with VMO coefficients in a half space. Zbl 1165.60330
Krylov, N. V.
6
2009
On linear elliptic and parabolic equations with growing drift in Sobolev spaces without weights. Zbl 1205.35328
Krylov, N. V.
4
2009
First derivatives estimates for finite-difference schemes. Zbl 1198.65165
Gyöngy, István; Krylov, Nicolai
2
2009
Higher order derivative estimates for finite-difference schemes for linear elliptic and parabolic equations. Zbl 1183.65107
Gyöngy, István; Krylov, Nicolai
2
2009
Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001
Krylov, N. V.
253
2008
On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra. Zbl 1183.15011
Krylov, N. V.
10
2008
A brief overview of the \(L_p\)-theory of SPDEs. Zbl 1224.60161
Krylov, Nicolai
4
2008
Large deviations for occupation times of Markov processes with \(L_{2}\) semigroups. Zbl 1157.60022
Jain, Naresh; Krylov, Nicolai
4
2008
On parabolic PDEs and SPDEs in Sobolev spaces \(W^2_p\) without and with weights. Zbl 1152.60046
Krylov, Nicolai V.
3
2008
On the rate of convergence of the finite-difference approximations for parabolic Bellman equations with constant coefficients. Zbl 1166.49026
Luo, Jun; Krylov, N. V.
1
2008
Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079
Krylov, N. V.
176
2007
Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others. Zbl 1138.35308
Kim, Doyoon; Krylov, N. V.
77
2007
Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052
Krylov, N. V.
72
2007
Parabolic equations with measurable coefficients. Zbl 1124.35024
Kim, Doyoon; Krylov, N. V.
59
2007
Stochastic evolution equations. Zbl 1130.60069
Krylov, Nicolai V.; Rozovskii, Boris L.
42
2007
The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains. Zbl 1127.65068
Dong, Hongjie; Krylov, Nicolai V.
24
2007
Maximum principle for SPDEs and its applications. Zbl 1135.60039
Krylov, Nicolai V.
18
2007
A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators. Zbl 1112.65087
Krylov, N. V.
8
2007
On time-inhomogeneous controlled diffusion processes in domains. Zbl 1127.93062
Dong, Hongjie; Krylov, N. V.
6
2007
...and 191 more Documents
all top 5

Cited by 3,577 Authors

117 Krylov, Nicolaĭ Vladimirovich
84 Röckner, Michael
76 Dong, Hongjie
64 Shaposhnikov, Stanislav V.
60 Bogachev, Vladimir Igorevich
47 Kim, KyeongHun
44 Gyöngy, István
43 Flandoli, Franco
37 Zhang, Xicheng
34 Zheng, Shenzhou
29 Kim, Doyoon
28 Lions, Pierre-Louis
28 Wang, Feng-Yu
25 Pragarauskas, Henrikas
23 Byun, Sun-Sig
23 Mikulevicius, Remigijus
23 Veretennikov, Alexander Yu.
22 Kim, Ildoo
22 Luo, Dejun
21 Jentzen, Arnulf
21 Veraar, Mark C.
20 Phan, Tuoc Van
19 Priola, Enrico
18 Arapostathis, Aristotle
18 Barbu, Viorel
18 Da Prato, Giuseppe
18 Dareiotis, Konstantinos Anastasios
18 Hofmanová, Martina
18 Reisinger, Christoph
17 Feireisl, Eduard
17 Trudinger, Neil Sidney
17 Wei, Jinlong
16 Breit, Dominic
16 Brzeźniak, Zdzisław
16 Ivochkina, Nina Mikhaĭlovna
16 Jakobsen, Espen Robstad
16 Liu, Wei
15 Borkar, Vivek Shripad
15 Delarue, François
15 Huang, Xing
15 Kim, Seick
15 Qiu, Jinniao
15 Wang, Lihe
15 Wang, Xu-Jia
14 Bahlali, Khaled
14 Gess, Benjamin
14 Karlsen, Kenneth Hvistendahl
14 Lee, Kijung
14 Lorenzi, Luca
14 Menozzi, Stéphane
14 Proske, Frank Norbert
13 da Silva, João Vítor
13 Gerencsér, Máté
13 Pardoux, Etienne
13 Yi, Yingfei
13 Zhang, Junjie
12 Arkhipova, Arina Alekseevna
12 Biswas, Anup
12 Gao, Hongjun
12 Lieberman, Gary M.
12 Safonov, Mikhail V.
12 Scarpa, Luca
12 Šiška, David
12 Tang, Shanjian
11 Deugoue, Gabriel
11 Dokuchaev, Nikolai G.
11 Du, Kai
11 Freidlin, Mark I.
11 Hutzenthaler, Martin
11 Nualart, David
11 Peng, Shige
11 Pham, Huyên
11 Pimentel, Edgard A.
11 Rozovskii, Boris L.
11 Sango, Mamadou
11 Xie, Longjie
11 Zhang, Tusheng S.
10 Bao, Jiguang
10 Bayraktar, Erhan
10 Caffarelli, Luis Ángel
10 Cerrai, Sandra
10 Crisan, Dan O.
10 Debussche, Arnaud
10 Grothaus, Martin
10 Hu, Mingshang
10 Karatzas, Ioannis
10 Kinzebulatov, Damir
10 Lee, Ki-Ahm
10 Lee, Mikyoung
10 Marinelli, Carlo
10 Mishura, Yuliya Stepanivna
10 Mohan, Manil Thankamani
10 Nazarov, Alexander I.
10 Palagachev, Dian K.
10 Razafimandimby, Paul André
10 Russo, Francesco
10 Stannat, Wilhelm
10 Świȩch, Andrzej
10 Teixeira, Eduardo V. O.
10 Tian, Hong
...and 3,477 more Authors
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Cited in 447 Serials

200 Journal of Differential Equations
187 Stochastic Processes and their Applications
141 Journal of Mathematical Analysis and Applications
116 Journal of Functional Analysis
87 Calculus of Variations and Partial Differential Equations
82 Stochastic and Partial Differential Equations. Analysis and Computations
73 Potential Analysis
72 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
68 Applied Mathematics and Optimization
67 Probability Theory and Related Fields
65 The Annals of Probability
62 SIAM Journal on Control and Optimization
61 Transactions of the American Mathematical Society
61 The Annals of Applied Probability
60 Communications in Partial Differential Equations
60 Journal of Mathematical Sciences (New York)
54 Archive for Rational Mechanics and Analysis
52 SIAM Journal on Mathematical Analysis
51 Stochastics and Dynamics
50 Stochastic Analysis and Applications
49 Journal of Evolution Equations
43 Stochastics
41 Journal de Mathématiques Pures et Appliquées. Neuvième Série
41 Discrete and Continuous Dynamical Systems
39 Doklady Mathematics
36 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
36 Electronic Journal of Probability
35 Advances in Mathematics
33 Proceedings of the American Mathematical Society
33 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
32 Journal of Theoretical Probability
31 NoDEA. Nonlinear Differential Equations and Applications
31 Communications on Pure and Applied Analysis
30 Mathematical Finance
27 Discrete and Continuous Dynamical Systems. Series B
26 The Journal of Geometric Analysis
23 Lithuanian Mathematical Journal
23 Stochastics
23 Mathematische Annalen
22 Systems & Control Letters
21 Journal of Computational and Applied Mathematics
21 SIAM Journal on Numerical Analysis
20 Statistics & Probability Letters
19 Mathematics of Computation
18 Annali di Matematica Pura ed Applicata. Serie Quarta
18 Mathematische Zeitschrift
18 Acta Applicandae Mathematicae
18 Differential Equations
18 Science China. Mathematics
17 Communications in Mathematical Physics
17 Communications on Pure and Applied Mathematics
17 Mathematical Notes
16 Nonlinearity
16 Journal für die Reine und Angewandte Mathematik
16 Siberian Mathematical Journal
16 Bernoulli
15 Bulletin des Sciences Mathématiques
15 Finance and Stochastics
15 Infinite Dimensional Analysis, Quantum Probability and Related Topics
15 Acta Mathematica Sinica. English Series
15 Nonlinear Analysis. Real World Applications
15 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
14 Duke Mathematical Journal
14 Mathematische Nachrichten
14 Journal of Scientific Computing
14 Journal of Dynamics and Differential Equations
13 Mathematical Methods in the Applied Sciences
13 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
13 Journal of Economic Dynamics & Control
13 St. Petersburg Mathematical Journal
13 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
12 Ukrainian Mathematical Journal
12 Manuscripta Mathematica
12 Journal of Nonlinear Science
12 Comptes Rendus. Mathématique. Académie des Sciences, Paris
12 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
12 SIAM Journal on Financial Mathematics
12 Nonlinear Analysis. Theory, Methods & Applications
11 Theory of Probability and its Applications
11 Journal of Optimization Theory and Applications
11 Journal of Soviet Mathematics
11 Journal of Mathematical Fluid Mechanics
11 Communications in Contemporary Mathematics
10 Computers & Mathematics with Applications
10 Applied Mathematics and Computation
10 Inventiones Mathematicae
10 Chinese Annals of Mathematics. Series B
10 Physica D
10 Stochastics and Stochastics Reports
10 Boundary Value Problems
9 Journal of Mathematical Physics
9 Journal of Statistical Physics
9 Automatica
9 Journal of Applied Probability
9 Numerische Mathematik
9 European Journal of Operational Research
9 Theory of Probability and Mathematical Statistics
9 Electronic Communications in Probability
9 Advanced Nonlinear Studies
8 Applicable Analysis
...and 347 more Serials
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Cited in 53 Fields

2,342 Partial differential equations (35-XX)
2,065 Probability theory and stochastic processes (60-XX)
451 Systems theory; control (93-XX)
387 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
385 Calculus of variations and optimal control; optimization (49-XX)
367 Numerical analysis (65-XX)
243 Fluid mechanics (76-XX)
222 Operator theory (47-XX)
209 Differential geometry (53-XX)
132 Functional analysis (46-XX)
131 Dynamical systems and ergodic theory (37-XX)
126 Ordinary differential equations (34-XX)
110 Global analysis, analysis on manifolds (58-XX)
108 Statistical mechanics, structure of matter (82-XX)
74 Operations research, mathematical programming (90-XX)
74 Biology and other natural sciences (92-XX)
70 Harmonic analysis on Euclidean spaces (42-XX)
60 Several complex variables and analytic spaces (32-XX)
59 Integral equations (45-XX)
57 Real functions (26-XX)
55 Statistics (62-XX)
47 Potential theory (31-XX)
37 Convex and discrete geometry (52-XX)
30 Mechanics of deformable solids (74-XX)
25 Measure and integration (28-XX)
25 Mechanics of particles and systems (70-XX)
23 Difference and functional equations (39-XX)
23 Computer science (68-XX)
23 Classical thermodynamics, heat transfer (80-XX)
18 Quantum theory (81-XX)
18 Geophysics (86-XX)
13 History and biography (01-XX)
12 Approximations and expansions (41-XX)
10 Functions of a complex variable (30-XX)
7 Algebraic geometry (14-XX)
7 Linear and multilinear algebra; matrix theory (15-XX)
6 Optics, electromagnetic theory (78-XX)
6 Information and communication theory, circuits (94-XX)
5 General and overarching topics; collections (00-XX)
5 Topological groups, Lie groups (22-XX)
5 Abstract harmonic analysis (43-XX)
5 Integral transforms, operational calculus (44-XX)
4 Combinatorics (05-XX)
4 Nonassociative rings and algebras (17-XX)
3 Special functions (33-XX)
2 Mathematical logic and foundations (03-XX)
2 Geometry (51-XX)
2 General topology (54-XX)
2 Relativity and gravitational theory (83-XX)
2 Astronomy and astrophysics (85-XX)
1 Associative rings and algebras (16-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)

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