## Schilling, René Leander

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 Author ID: schilling.rene-leander Published as: Schilling, René L.; Schilling, R. L.; Schilling, Rene L.; Schilling, René; Schilling, René Leander more...less Homepage: https://tu-dresden.de/mn/math/stochastik/schilling External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef
 Documents Indexed: 108 Publications since 1994, including 15 Books 2 Contributions as Editor Reviewing Activity: 233 Reviews Co-Authors: 55 Co-Authors with 90 Joint Publications 1,383 Co-Co-Authors
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### Co-Authors

 20 single-authored 13 Jacob, Niels 12 Wang, Jian 10 Böttcher, Björn 8 Deng, Changsong 8 Knopova, Victoria Pavlovna 7 Kühn, Franziska 7 Lindner, Felix 5 Cioica, Petru A. 5 Dahlke, Stephan 5 Kinzel, Stefan 5 Raasch, Thorsten 5 Ritter, Klaus 5 Vondraček, Zoran 4 Kinderknecht, Yana A. 4 Döhring, Nicolas 4 Smolyanov, Oleg Georgievich 3 Meerschaert, Mark Marvin 3 Uemura, Toshihiro 2 Burdzy, Krzysztof 2 Farkas, Walter 2 Feller, William 2 Friedrich, Ulrich 2 Keller-Ressel, Martin 2 Khoshnevisan, Davar 2 Kolokoltsov, Vassili N. 2 Kovács, Mihály 2 Kulczycki, Tadeusz 2 Partzsch, Lothar 2 Porcu, Emilio 2 Sikorskii, Alla 2 Song, Renming 2 Song, Yanhong 2 Woyczynski, Wojbor A. 1 Bäumer, Boris 1 Berger, David 1 Germano, Guido 1 Kaleta, Kamil 1 Kondrat’yev, Yuriĭ Grygorovych 1 Kulik, Alexey M. 1 Landwehr, Sandra 1 Leonenko, Nikolai N. 1 Liang, Mingjie 1 Lifshits, Mikhail A. 1 Magdziarz, Marcin 1 Mimica, Ante 1 Mishura, Yuliya Stepanivna 1 Politi, Mauro 1 Quer-Sardanyons, Lluís 1 Sandrić, Nikola 1 Scalas, Enrico 1 Schnurr, Alexander 1 Straka, Peter 1 Sztonyk, Paweł 1 Tyukov, Alexei E. 1 Tyurin, Ilya 1 Utzet, Frederic 1 Xiao, Yimin 1 Xu, Lihu
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### Serials

 5 Stochastic Processes and their Applications 4 Transactions of the American Mathematical Society 4 Bernoulli 4 De Gruyter Studium 3 Journal of Theoretical Probability 3 Potential Analysis 3 Electronic Journal of Probability 2 Advances in Applied Probability 2 Studia Mathematica 2 Dissertationes Mathematicae 2 Journal of Functional Analysis 2 Mathematische Nachrichten 2 Zeitschrift für Analysis und ihre Anwendungen 2 Statistics & Probability Letters 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 Expositiones Mathematicae 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 De Gruyter Studies in Mathematics 2 De Gruyter Graduate 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 The Annals of Statistics 1 BIT 1 Bulletin of the London Mathematical Society 1 Integral Equations and Operator Theory 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Publicationes Mathematicae Debrecen 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tôhoku Mathematical Journal. Second Series 1 Probability and Mathematical Statistics 1 Stochastic Analysis and Applications 1 Acta Applicandae Mathematicae 1 Probability Theory and Related Fields 1 Journal of the Australian Mathematical Society. Series A 1 Stochastics and Stochastics Reports 1 Theory of Probability and Mathematical Statistics 1 Russian Journal of Mathematical Physics 1 Electronic Communications in Probability 1 Doklady Mathematics 1 Nonlinear Dynamics 1 Positivity 1 Fractional Calculus & Applied Analysis 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Evolution Equations 1 Foundations of Computational Mathematics 1 Stochastics and Dynamics 1 Mediterranean Journal of Mathematics 1 Lecture Notes in Mathematics 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Science China. Mathematics 1 Communications in Applied and Industrial Mathematics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Modern Stochastics. Theory and Applications 1 Advanced Courses in Mathematics – CRM Barcelona 1 De Gruyter Textbook
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### Fields

 96 Probability theory and stochastic processes (60-XX) 29 Operator theory (47-XX) 25 Partial differential equations (35-XX) 16 Potential theory (31-XX) 9 Measure and integration (28-XX) 8 Functional analysis (46-XX) 8 Numerical analysis (65-XX) 5 Real functions (26-XX) 4 Statistics (62-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX)

### Citations contained in zbMATH Open

89 Publications have been cited 1,305 times in 797 Documents Cited by Year
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
2012
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
2010
Growth and Hölder conditions for the sample paths of Feller processes. Zbl 0930.60013
Schilling, René L.
1998
Lévy matters III. Lévy-type processes: construction, approximation and sample path properties. Zbl 1384.60004
Böttcher, Björn; Schilling, René; Wang, Jian
2013
A note on the existence of transition probability densities of Lévy processes. Zbl 1269.60050
Knopova, Victoria; Schilling, René L.
2013
Coupling property and gradient estimates of Lévy processes via the symbol. Zbl 1263.60045
Schilling, René L.; Sztonyk, Paweł; Wang, Jian
2012
The symbol associated with the solution of a stochastic differential equation. Zbl 1226.60116
Schilling, Rene L.; Schnurr, Alexander
2010
Conservativeness and extensions of Feller semigroups. Zbl 0919.47033
Schilling, René L.
1998
Function spaces related to continuous negative definite functions: $$\psi$$-Bessel potential spaces. Zbl 0990.46018
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Asymptotic properties of Brownian motion delayed by inverse subordinators. Zbl 1329.60291
Magdziarz, Marcin; Schilling, René L.
2015
Subordination in the sense of Bochner and a related functional calculus. Zbl 0920.47039
Schilling, René L.
1998
Lévy-type processes and pseudodifferential operators. Zbl 0984.60054
Jacob, Niels; Schilling, René L.
2001
On the Feller property of Dirichlet forms generated by pseudo differential operators. Zbl 1141.31006
Schilling, René L.; Uemura, Toshihiro
2007
Measures, integrals and martingales. Zbl 1084.28001
Schilling, René L.
2005
Correlation structure of time-changed Lévy processes. Zbl 1329.60118
Leonenko, Nikolai N.; Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2014
Transition density estimates for a class of Lévy and Lévy-type processes. Zbl 1242.60082
Knopova, Viktorya; Schilling, René L.
2012
Measures, integrals and martingales. 2nd edition. Zbl 1360.28001
Schilling, René L.
2017
A geometric interpretation of the transition density of a symmetric Lévy process. Zbl 1279.60097
Jacob, Niels; Knopova, Victorya; Landwehr, Sandra; Schilling, René L.
2012
On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes. Zbl 1247.60113
Schilling, René L.; Wang, Jian
2012
Some theorems on Feller processes: transience, local times and ultracontractivity. Zbl 1282.60070
Schilling, René L.; Wang, Jian
2013
On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes. Zbl 1328.60118
Deng, Chang-Song; Schilling, René L.
2015
Constructions of coupling processes for Lévy processes. Zbl 1217.60035
Böttcher, Björn; Schilling, René L.; Wang, Jian
2011
On the coupling property of Lévy processes. Zbl 1268.60061
Schilling, René L.; Wang, Jian
2011
Approximation of Feller processes by Markov chains with Lévy increments. Zbl 1168.60359
Böttcher, Björn; Schilling, René L.
2009
Reflected spectrally negative stable processes and their governing equations. Zbl 1378.60075
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.; Schilling, René L.; Straka, Peter
2016
Functional inequalities and subordination: Stability of Nash and Poincaré inequalities. Zbl 1259.47058
Schilling, René L.; Wang, Jian
2012
Weak order for the discretization of the stochastic heat equation driven by impulsive noise. Zbl 1263.60058
Lindner, Felix; Schilling, René L.
2013
Strong Feller continuity of Feller processes and semigroups. Zbl 1258.60047
Schilling, René L.; Wang, Jian
2012
Brownian motion. An introduction to stochastic processes. With contributions by Björn Böttcher. 2nd revised and extended ed. Zbl 1283.60003
Schilling, René L.; Partzsch, Lothar
2014
Feller semigroup, $$L^p$$-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols. Zbl 0978.47031
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Some Dirichlet spaces obtained by subordinate reflected diffusions. Zbl 0922.31011
Jacob, Niels; Schilling, René L.
1999
Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations. Zbl 1273.47070
Butko, Yana A.; Schilling, René L.; Smolyanov, Oleg G.
2012
Function spaces as path spaces of Feller processes. Zbl 0970.60043
Schilling, René L.
2000
On Feller processes with sample paths in Besov spaces. Zbl 0888.60036
Schilling, René L.
1997
Feller processes generated by pseudo-differential operators: On the Hausdorff dimension of their sample paths. Zbl 0910.60028
Schilling, René L.
1998
Feynman formulae for Feller semigroups. Zbl 1213.47047
Butko, Ya. A.; Smolyanov, O. G.; Schilling, R. L.
2010
Conservativeness of semigroups generated by pseudo differential operators. Zbl 0917.60066
Schilling, René L.
1998
Stochastic solutions for fractional wave equations. Zbl 1345.35134
Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2015
On the domain of fractional Laplacians and related generators of Feller processes. Zbl 1464.60044
Kühn, Franziska; Schilling, René L.
2019
From Schoenberg to Pick-Nevanlinna: toward a complete picture of the variogram class. Zbl 1280.60032
Porcu, Emilio; Schilling, René L.
2011
Function spaces as Dirichlet spaces (about a paper by Maz’ya and Nagel). Zbl 1107.46027
Jacob, Niels; Schilling, René L.
2005
Brownian motion. An introduction to stochastic processes. With a chapter on simulation by Björn Böttcher. Zbl 1258.60002
Schilling, René L.; Partzsch, Lothar
2012
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains. Zbl 1250.60026
Cioica, Petru A.; Dahlke, Stephan; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2011
From Lévy-type processes to parabolic SPDEs. Edited by Lluís Quer-Sardanyons and Frederic Utzet. Zbl 1382.60005
Khoshnevisan, Davar; Schilling, René
2016
Lower bounded semi-Dirichlet forms associated with Lévy type operators. Zbl 1336.31030
Schilling, René L.; Wang, Jian
2015
Towards an $$L^p$$ potential theory for sub-Markovian semigroups: kernels and capacities. Zbl 1104.31007
Jacob, Niels; Schilling, René L.
2006
Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs. Zbl 1422.60097
Kühn, Franziska; Schilling, René L.
2019
Feynman formulas and path integrals for some evolution semigroups related to $$\tau$$-quantization. Zbl 1311.58006
Böttcher, B.; Butko, Ya. A.; Schilling, R. L.; Smolyanov, O. G.
2011
On the structure of the domain of a symmetric jump-type Dirichlet form. Zbl 1241.31013
Schilling, René L.; Uemura, Toshihiro
2012
Subgeometric rates of convergence for Markov processes under subordination. Zbl 1425.60064
Deng, Chang-Song; Schilling, René L.; Song, Yan-Hong
2017
Distance multivariance: new dependence measures for random vectors. Zbl 1467.62104
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2019
Packing dimension profiles and Lévy processes. Zbl 1266.60071
Khoshnevisan, D.; Schilling, R. L.; Xiao, Y.
2012
An analytic proof of the Lévy-Khinchin formula on $$R^n$$. Zbl 0928.42003
Jacob, Niels; Schilling, René L.
1998
Dirichlet operators and the positive maximum principle. Zbl 0994.31003
Schilling, Rene L.
2001
Adaptive wavelet methods for the stochastic Poisson equation. Zbl 1260.65003
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2012
On the domain of the generator of a subordinate semigroup. Zbl 0857.47025
Schilling, René L.
1996
Harnack inequalities for SDEs driven by time-changed fractional Brownian motions. Zbl 1386.60147
Deng, Chang-Song; Schilling, René L.
2017
Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass. Zbl 1226.81114
Butko, Yana A.; Schilling, Rene L.; Smolyanov, Oleg G.
2011
Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noise. Zbl 1335.60131
Kovács, Mihály; Lindner, Felix; Schilling, René L.
2015
A unified approach to coupling SDEs driven by Lévy noise and some applications. Zbl 1465.60039
Liang, Mingjie; Schilling, René L.; Wang, Jian
2020
Sobolev embedding for stochastic processes. Zbl 0970.60044
Schilling, René L.
2000
On the path behavior of Markov processes comparable with Lévy processes. (Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy-Prozessen vergleichbar sind.) Zbl 0805.60032
Schilling, René Leander
1994
On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motion. Zbl 1329.60289
Deng, Chang-Song; Schilling, René L.
2015
Convergence analysis of spatially adaptive Rothe methods. Zbl 1309.65107
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Friedrich, Ulrich; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form. Zbl 0970.31008
Jacob, N.; Schilling, R. L.
2000
Lower bounds of the Hausdorff dimension for the images of Feller processes. Zbl 1351.60043
Knopova, V.; Schilling, R. L.; Wang, J.
2015
On the small-time behaviour of Lévy-type processes. Zbl 1309.60027
Knopova, Victoria; Schilling, René L.
2014
A note on invariant sets. Zbl 1077.47045
Schilling, René L.
2004
A probabilistic proof of Schoenberg’s theorem. Zbl 1486.60032
Kühn, Franziska; Schilling, René L.
2019
A probabilistic inequality related to negative definite functions. Zbl 1270.60030
Lifshits, Mikhail; Schilling, René L.; Tyurin, Ilya
2013
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025
Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E.
2004
Correction to: “Subgeometric rates of convergence for Markov processes under subordination”. Zbl 1430.60062
Deng, C.-S.; Schilling, R. L.; Song, Y.-H.
2018
Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators. Zbl 07210214
Kaleta, Kamil; Schilling, René L.
2020
Estimates for Feller semigroups generated by pseudodifferential operators. Zbl 0931.35204
Jacob, Niels; Schilling, René L.
1996
Comparable processes and the Hausdorff dimension of their sample paths. Zbl 0888.60035
Schilling, René L.
1996
Subordination in the sense of S. Bochner – An approach through pseudo differential operators. Zbl 0923.47023
Jacob, Niels; Schilling, René L.
1996
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Zbl 1221.60129
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.
2010
Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042
Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E.
2002
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance. Zbl 1417.62158
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2018
On level and collision sets of some Feller processes. Zbl 1351.60044
Knopova, Victoria; Schilling, René L.
2015
Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process. Zbl 1359.60054
Schilling, René L.; Vondraček, Zoran
2017
Construction and heat kernel estimates of general stable-like Markov processes. Zbl 1485.60072
Knopova, Victoria; Kulik, Alexei; Schilling, René L.
2021
Exact asymptotic formulas for the heat kernels of space and time-fractional equations. Zbl 1434.60206
Deng, Chang-Song; Schilling, René L.
2019
Selected papers I. Edited by René L. Schilling, Zoran Vondraček and Wojbor A. Woyczynski. Zbl 1315.01001
Feller, William
2015
Adaptive wavelet methods for SPDEs. Zbl 1317.60084
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
When does a càdlàg process have continuous sample paths? Zbl 0830.60036
Schilling, René L.
1994
On a Poincaré-type inequality for energy forms in $$L^p$$. Zbl 1150.31003
Jacob, Niels; Schilling, René L.
2007
Stationary distributions for jump processes with inert drift. Zbl 1291.60170
Burdzy, K.; Kulczycki, T.; Schilling, R. L.
2013
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of stochastic partial differential equations. Zbl 1337.60160
Cioica, P. A.; Dahlke, S.; Döhring, N.; Friedrich, U.; Kinzel, S.; Lindner, F.; Raasch, T.; Ritter, K.; Schilling, René L.
2016
Construction and heat kernel estimates of general stable-like Markov processes. Zbl 1485.60072
Knopova, Victoria; Kulik, Alexei; Schilling, René L.
2021
A unified approach to coupling SDEs driven by Lévy noise and some applications. Zbl 1465.60039
Liang, Mingjie; Schilling, René L.; Wang, Jian
2020
Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators. Zbl 07210214
Kaleta, Kamil; Schilling, René L.
2020
On the domain of fractional Laplacians and related generators of Feller processes. Zbl 1464.60044
Kühn, Franziska; Schilling, René L.
2019
Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs. Zbl 1422.60097
Kühn, Franziska; Schilling, René L.
2019
Distance multivariance: new dependence measures for random vectors. Zbl 1467.62104
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2019
A probabilistic proof of Schoenberg’s theorem. Zbl 1486.60032
Kühn, Franziska; Schilling, René L.
2019
Exact asymptotic formulas for the heat kernels of space and time-fractional equations. Zbl 1434.60206
Deng, Chang-Song; Schilling, René L.
2019
Correction to: “Subgeometric rates of convergence for Markov processes under subordination”. Zbl 1430.60062
Deng, C.-S.; Schilling, R. L.; Song, Y.-H.
2018
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance. Zbl 1417.62158
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2018
Measures, integrals and martingales. 2nd edition. Zbl 1360.28001
Schilling, René L.
2017
Subgeometric rates of convergence for Markov processes under subordination. Zbl 1425.60064
Deng, Chang-Song; Schilling, René L.; Song, Yan-Hong
2017
Harnack inequalities for SDEs driven by time-changed fractional Brownian motions. Zbl 1386.60147
Deng, Chang-Song; Schilling, René L.
2017
Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process. Zbl 1359.60054
Schilling, René L.; Vondraček, Zoran
2017
Reflected spectrally negative stable processes and their governing equations. Zbl 1378.60075
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.; Schilling, René L.; Straka, Peter
2016
From Lévy-type processes to parabolic SPDEs. Edited by Lluís Quer-Sardanyons and Frederic Utzet. Zbl 1382.60005
Khoshnevisan, Davar; Schilling, René
2016
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of stochastic partial differential equations. Zbl 1337.60160
Cioica, P. A.; Dahlke, S.; Döhring, N.; Friedrich, U.; Kinzel, S.; Lindner, F.; Raasch, T.; Ritter, K.; Schilling, René L.
2016
Asymptotic properties of Brownian motion delayed by inverse subordinators. Zbl 1329.60291
Magdziarz, Marcin; Schilling, René L.
2015
On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes. Zbl 1328.60118
Deng, Chang-Song; Schilling, René L.
2015
Stochastic solutions for fractional wave equations. Zbl 1345.35134
Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2015
Lower bounded semi-Dirichlet forms associated with Lévy type operators. Zbl 1336.31030
Schilling, René L.; Wang, Jian
2015
Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noise. Zbl 1335.60131
Kovács, Mihály; Lindner, Felix; Schilling, René L.
2015
On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motion. Zbl 1329.60289
Deng, Chang-Song; Schilling, René L.
2015
Lower bounds of the Hausdorff dimension for the images of Feller processes. Zbl 1351.60043
Knopova, V.; Schilling, R. L.; Wang, J.
2015
On level and collision sets of some Feller processes. Zbl 1351.60044
Knopova, Victoria; Schilling, René L.
2015
Selected papers I. Edited by René L. Schilling, Zoran Vondraček and Wojbor A. Woyczynski. Zbl 1315.01001
Feller, William
2015
Correlation structure of time-changed Lévy processes. Zbl 1329.60118
Leonenko, Nikolai N.; Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2014
Brownian motion. An introduction to stochastic processes. With contributions by Björn Böttcher. 2nd revised and extended ed. Zbl 1283.60003
Schilling, René L.; Partzsch, Lothar
2014
Convergence analysis of spatially adaptive Rothe methods. Zbl 1309.65107
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Friedrich, Ulrich; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
On the small-time behaviour of Lévy-type processes. Zbl 1309.60027
Knopova, Victoria; Schilling, René L.
2014
Adaptive wavelet methods for SPDEs. Zbl 1317.60084
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
Lévy matters III. Lévy-type processes: construction, approximation and sample path properties. Zbl 1384.60004
Böttcher, Björn; Schilling, René; Wang, Jian
2013
A note on the existence of transition probability densities of Lévy processes. Zbl 1269.60050
Knopova, Victoria; Schilling, René L.
2013
Some theorems on Feller processes: transience, local times and ultracontractivity. Zbl 1282.60070
Schilling, René L.; Wang, Jian
2013
Weak order for the discretization of the stochastic heat equation driven by impulsive noise. Zbl 1263.60058
Lindner, Felix; Schilling, René L.
2013
A probabilistic inequality related to negative definite functions. Zbl 1270.60030
Lifshits, Mikhail; Schilling, René L.; Tyurin, Ilya
2013
Stationary distributions for jump processes with inert drift. Zbl 1291.60170
Burdzy, K.; Kulczycki, T.; Schilling, R. L.
2013
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
2012
Coupling property and gradient estimates of Lévy processes via the symbol. Zbl 1263.60045
Schilling, René L.; Sztonyk, Paweł; Wang, Jian
2012
Transition density estimates for a class of Lévy and Lévy-type processes. Zbl 1242.60082
Knopova, Viktorya; Schilling, René L.
2012
A geometric interpretation of the transition density of a symmetric Lévy process. Zbl 1279.60097
Jacob, Niels; Knopova, Victorya; Landwehr, Sandra; Schilling, René L.
2012
On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes. Zbl 1247.60113
Schilling, René L.; Wang, Jian
2012
Functional inequalities and subordination: Stability of Nash and Poincaré inequalities. Zbl 1259.47058
Schilling, René L.; Wang, Jian
2012
Strong Feller continuity of Feller processes and semigroups. Zbl 1258.60047
Schilling, René L.; Wang, Jian
2012
Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations. Zbl 1273.47070
Butko, Yana A.; Schilling, René L.; Smolyanov, Oleg G.
2012
Brownian motion. An introduction to stochastic processes. With a chapter on simulation by Björn Böttcher. Zbl 1258.60002
Schilling, René L.; Partzsch, Lothar
2012
On the structure of the domain of a symmetric jump-type Dirichlet form. Zbl 1241.31013
Schilling, René L.; Uemura, Toshihiro
2012
Packing dimension profiles and Lévy processes. Zbl 1266.60071
Khoshnevisan, D.; Schilling, R. L.; Xiao, Y.
2012
Adaptive wavelet methods for the stochastic Poisson equation. Zbl 1260.65003
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2012
Constructions of coupling processes for Lévy processes. Zbl 1217.60035
Böttcher, Björn; Schilling, René L.; Wang, Jian
2011
On the coupling property of Lévy processes. Zbl 1268.60061
Schilling, René L.; Wang, Jian
2011
From Schoenberg to Pick-Nevanlinna: toward a complete picture of the variogram class. Zbl 1280.60032
Porcu, Emilio; Schilling, René L.
2011
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains. Zbl 1250.60026
Cioica, Petru A.; Dahlke, Stephan; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2011
Feynman formulas and path integrals for some evolution semigroups related to $$\tau$$-quantization. Zbl 1311.58006
Böttcher, B.; Butko, Ya. A.; Schilling, R. L.; Smolyanov, O. G.
2011
Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass. Zbl 1226.81114
Butko, Yana A.; Schilling, Rene L.; Smolyanov, Oleg G.
2011
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
2010
The symbol associated with the solution of a stochastic differential equation. Zbl 1226.60116
Schilling, Rene L.; Schnurr, Alexander
2010
Feynman formulae for Feller semigroups. Zbl 1213.47047
Butko, Ya. A.; Smolyanov, O. G.; Schilling, R. L.
2010
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Zbl 1221.60129
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.
2010
Approximation of Feller processes by Markov chains with Lévy increments. Zbl 1168.60359
Böttcher, Björn; Schilling, René L.
2009
On the Feller property of Dirichlet forms generated by pseudo differential operators. Zbl 1141.31006
Schilling, René L.; Uemura, Toshihiro
2007
On a Poincaré-type inequality for energy forms in $$L^p$$. Zbl 1150.31003
Jacob, Niels; Schilling, René L.
2007
Towards an $$L^p$$ potential theory for sub-Markovian semigroups: kernels and capacities. Zbl 1104.31007
Jacob, Niels; Schilling, René L.
2006
Measures, integrals and martingales. Zbl 1084.28001
Schilling, René L.
2005
Function spaces as Dirichlet spaces (about a paper by Maz’ya and Nagel). Zbl 1107.46027
Jacob, Niels; Schilling, René L.
2005
A note on invariant sets. Zbl 1077.47045
Schilling, René L.
2004
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025
Kolokol&rsquo;tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E.
2004
Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042
Kolokol&rsquo;tsov, V. N.; Schilling, R. L.; Tyukov, A. E.
2002
Function spaces related to continuous negative definite functions: $$\psi$$-Bessel potential spaces. Zbl 0990.46018
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Lévy-type processes and pseudodifferential operators. Zbl 0984.60054
Jacob, Niels; Schilling, René L.
2001
Feller semigroup, $$L^p$$-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols. Zbl 0978.47031
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Dirichlet operators and the positive maximum principle. Zbl 0994.31003
Schilling, Rene L.
2001
Function spaces as path spaces of Feller processes. Zbl 0970.60043
Schilling, René L.
2000
Sobolev embedding for stochastic processes. Zbl 0970.60044
Schilling, René L.
2000
Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form. Zbl 0970.31008
Jacob, N.; Schilling, R. L.
2000
Some Dirichlet spaces obtained by subordinate reflected diffusions. Zbl 0922.31011
Jacob, Niels; Schilling, René L.
1999
Growth and Hölder conditions for the sample paths of Feller processes. Zbl 0930.60013
Schilling, René L.
1998
Conservativeness and extensions of Feller semigroups. Zbl 0919.47033
Schilling, René L.
1998
Subordination in the sense of Bochner and a related functional calculus. Zbl 0920.47039
Schilling, René L.
1998
Feller processes generated by pseudo-differential operators: On the Hausdorff dimension of their sample paths. Zbl 0910.60028
Schilling, René L.
1998
Conservativeness of semigroups generated by pseudo differential operators. Zbl 0917.60066
Schilling, René L.
1998
An analytic proof of the Lévy-Khinchin formula on $$R^n$$. Zbl 0928.42003
Jacob, Niels; Schilling, René L.
1998
On Feller processes with sample paths in Besov spaces. Zbl 0888.60036
Schilling, René L.
1997
On the domain of the generator of a subordinate semigroup. Zbl 0857.47025
Schilling, René L.
1996
Estimates for Feller semigroups generated by pseudodifferential operators. Zbl 0931.35204
Jacob, Niels; Schilling, René L.
1996
Comparable processes and the Hausdorff dimension of their sample paths. Zbl 0888.60035
Schilling, René L.
1996
Subordination in the sense of S. Bochner – An approach through pseudo differential operators. Zbl 0923.47023
Jacob, Niels; Schilling, René L.
1996
On the path behavior of Markov processes comparable with Lévy processes. (Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy-Prozessen vergleichbar sind.) Zbl 0805.60032
Schilling, René Leander
1994
When does a càdlàg process have continuous sample paths? Zbl 0830.60036
Schilling, René L.
1994
all top 5

### Cited by 883 Authors

 47 Schilling, René Leander 39 Wang, Jian 18 Chen, Zhen-Qing 18 Kim, Panki 18 Kühn, Franziska 15 Qi, Feng 14 Grzywny, Tomasz 14 Kaleta, Kamil 13 Song, Renming 12 Bogdan, Krzysztof 12 Leonenko, Nikolai N. 12 Vondraček, Zoran 11 Jacob, Niels 11 Kovács, Mihály 11 Sandrić, Nikola 10 Böttcher, Björn 10 Lörinczi, József 10 Meerschaert, Mark Marvin 10 Sztonyk, Paweł 9 Guo, Bai-Ni 9 Knopova, Victoria Pavlovna 9 Kumagai, Takashi 9 Porcu, Emilio 9 Uemura, Toshihiro 8 Kinderknecht, Yana A. 8 Deng, Changsong 8 Ryznar, Michał 7 Ascione, Giacomo 7 Bäumer, Boris 7 Fageot, Julien 7 Kulczycki, Tadeusz 7 Patie, Pierre 7 Pirozzi, Enrica 7 Schnurr, Alexander 7 Smolyanov, Oleg Georgievich 7 Toaldo, Bruno 7 Xiao, Yimin 6 Bazhlekova, Emilia G. 6 D’Ovidio, Mirko 6 Kaßmann, Moritz 6 Kwaśnicki, Mateusz 6 Menegatto, Valdir Antonio 6 Remizov, Ivan D. 6 Röckner, Michael 6 Wang, Feng-Yu 5 Anh, Vo V. 5 Behme, Anita Diana 5 Cygan, Wojciech 5 Dahlke, Stephan 5 Gomilko, Alexandre M. 5 Hanyga, Andrzej 5 Kim, KyeongHun 5 Kondrat’yev, Yuriĭ Grygorovych 5 Lindner, Felix 5 Maheshwari, Aditya 5 Mikulevicius, Remigijus 5 Mimica, Ante 5 Nane, Erkan 5 Pietruska-Pałuba, Katarzyna 5 Sakbaev, Vsevolod Zhanovich 5 Shiozawa, Yuichi 5 Tomilov, Yuri 5 Toniazzi, Lorenzo 5 Unser, Michael A. 5 Vellaisamy, Palaniappan 5 Yang, Xiaochuan 4 Applebaum, David B. 4 Beghin, Luisa 4 Chen, Xin 4 da Silva, José Luís 4 Evans, Kristian P. 4 Hausenblas, Erika 4 Jentzen, Arnulf 4 Kataria, Kuldeep Kumar 4 Khandakar, Mostafizar 4 Kim, Ildoo 4 Larsson, Stig 4 Mai, Jan-Frederik 4 Majka, Mateusz B. 4 Mishura, Yuliya Stepanivna 4 Ricciuti, Costantino 4 Ruiz-Medina, María Dolores 4 Sun, Wei 4 Zhang, Xicheng 4 Zhigljavsky, Anatoly A. 3 Albeverio, Sergio A. 3 Bañuelos, Rodrigo 3 Bazhlekov, Ivan B. 3 Biswas, Anup 3 Cioica, Petru A. 3 Deng, Weihua 3 Döhring, Nicolas 3 Du, Qiang 3 Emery, Xavier 3 Fahrenwaldt, Matthias Albrecht 3 Farkas, Walter 3 Jiao, Yong 3 Kaneko, Hiroshi 3 Karp, Dmitriĭ Borisovich 3 Kinzel, Stefan ...and 783 more Authors
all top 5

### Cited in 244 Serials

 47 Stochastic Processes and their Applications 33 Journal of Mathematical Analysis and Applications 33 Journal of Theoretical Probability 29 Potential Analysis 26 Transactions of the American Mathematical Society 22 Journal of Functional Analysis 22 Statistics & Probability Letters 22 Bernoulli 19 Fractional Calculus & Applied Analysis 15 Journal of Differential Equations 13 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 13 Electronic Journal of Probability 12 Stochastic Analysis and Applications 11 Journal of Computational and Applied Mathematics 9 Mathematische Nachrichten 9 Proceedings of the American Mathematical Society 9 Journal of Evolution Equations 8 Journal of Statistical Physics 8 Chaos, Solitons and Fractals 8 Probability Theory and Related Fields 7 The Annals of Probability 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Integral Equations and Operator Theory 6 Journal of Applied Probability 6 Theory of Probability and Mathematical Statistics 6 Stochastics and Dynamics 6 ALEA. Latin American Journal of Probability and Mathematical Statistics 5 Communications in Mathematical Physics 5 Studia Mathematica 5 The Annals of Applied Probability 5 Acta Mathematica Sinica. English Series 5 Science China. Mathematics 5 Stochastic and Partial Differential Equations. Analysis and Computations 5 Modern Stochastics. Theory and Applications 4 Advances in Applied Probability 4 Journal d’Analyse Mathématique 4 Advances in Mathematics 4 BIT 4 Osaka Journal of Mathematics 4 Semigroup Forum 4 Probability and Mathematical Statistics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Finance and Stochastics 4 Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 Mediterranean Journal of Mathematics 4 Problemy Analiza. Issues of Analysis 3 Computers & Mathematics with Applications 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Theory of Probability and its Applications 3 Applied Mathematics and Computation 3 Mathematische Annalen 3 Mathematische Zeitschrift 3 Memoirs of the American Mathematical Society 3 Results in Mathematics 3 Tôhoku Mathematical Journal. Second Series 3 Acta Applicandae Mathematicae 3 Applied Numerical Mathematics 3 Forum Mathematicum 3 Communications in Statistics. Theory and Methods 3 SIAM Journal on Mathematical Analysis 3 Russian Journal of Mathematical Physics 3 Electronic Communications in Probability 3 The Journal of Fourier Analysis and Applications 3 Positivity 3 Communications in Nonlinear Science and Numerical Simulation 3 Communications in Contemporary Mathematics 3 Stochastics 3 Journal of Physics A: Mathematical and Theoretical 3 Analysis and Mathematical Physics 3 Dependence Modeling 3 SIAM/ASA Journal on Uncertainty Quantification 2 International Journal of Theoretical Physics 2 Journal of Mathematical Physics 2 Metrika 2 Physica A 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Statistics 2 Applied Mathematics and Optimization 2 Automatica 2 Journal of Approximation Theory 2 Journal of Econometrics 2 Journal of the London Mathematical Society. Second Series 2 Journal of the Mathematical Society of Japan 2 Journal of Multivariate Analysis 2 Journal of Optimization Theory and Applications 2 Proceedings of the London Mathematical Society. Third Series 2 Quarterly of Applied Mathematics 2 SIAM Journal on Control and Optimization 2 Zeitschrift für Analysis und ihre Anwendungen 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Acta Mathematicae Applicatae Sinica. English Series 2 Constructive Approximation 2 Statistical Science 2 Linear Algebra and its Applications 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Statistical Papers 2 Doklady Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Vietnam Journal of Mathematics 2 Journal of Inequalities and Applications ...and 144 more Serials
all top 5

### Cited in 44 Fields

 549 Probability theory and stochastic processes (60-XX) 214 Partial differential equations (35-XX) 157 Operator theory (47-XX) 80 Real functions (26-XX) 61 Potential theory (31-XX) 60 Numerical analysis (65-XX) 51 Functional analysis (46-XX) 51 Statistics (62-XX) 50 Special functions (33-XX) 45 Harmonic analysis on Euclidean spaces (42-XX) 33 Integral equations (45-XX) 30 Integral transforms, operational calculus (44-XX) 26 Measure and integration (28-XX) 24 Ordinary differential equations (34-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Statistical mechanics, structure of matter (82-XX) 16 Abstract harmonic analysis (43-XX) 14 Combinatorics (05-XX) 14 Quantum theory (81-XX) 13 Functions of a complex variable (30-XX) 12 Number theory (11-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Approximations and expansions (41-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 Mechanics of deformable solids (74-XX) 9 Systems theory; control (93-XX) 8 Difference and functional equations (39-XX) 8 Fluid mechanics (76-XX) 7 Biology and other natural sciences (92-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Computer science (68-XX) 5 Geophysics (86-XX) 5 Operations research, mathematical programming (90-XX) 4 Sequences, series, summability (40-XX) 4 Information and communication theory, circuits (94-XX) 3 Mathematical logic and foundations (03-XX) 3 Differential geometry (53-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 1 Algebraic geometry (14-XX) 1 Manifolds and cell complexes (57-XX) 1 Optics, electromagnetic theory (78-XX)

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