Michael Röckner
PEVZ-ID
322 Publikationen
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993907Barbu, Viorel, and Röckner, Michael. 2024. “Markov Processes Associated with Nonlinear Fokker-Planck Equations”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts, ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:189-195. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993906Barbu, Viorel, and Röckner, Michael. 2024. “Time Dependent Fokker-Planck Equations”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts, ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:123-145. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993905Barbu, Viorel, and Röckner, Michael. 2024. “Appendix”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts , ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:197-203. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993902Barbu, Viorel, and Röckner, Michael. 2024. “Convergence to Equilibrium of Nonlinear Fokker-Planck Flows”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts, ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:147-188. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993899Barbu, Viorel, and Röckner, Michael. 2024. “Existence of Nonlinear Fokker-Planck Flows”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts, ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:13-122. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993901Barbu, Viorel, and Röckner, Michael. 2024. “Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts. Introduction”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts, ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:1-11. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2993900Barbu, Viorel, and Röckner, Michael. 2024. “Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts. Preface”. In Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts , ed. Jean-Michel Morel, Kowloon Tong, and Bernard Teissier, 2353:v-vi. Lecture Notes in Mathematics. Cham: Springer .
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2024 | Diskussionspapier | Veröffentlicht | PUB-ID: 2990509Federico, Salvatore, Ferrari, Giorgio, Riedel, Frank, and Röckner, Michael. 2024. Variational Inequalities and Smooth-Fit Principle for Singular Stochastic Control Problems in Hilbert Spaces. Vol. 692. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
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2023 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2987158Bogachev, V. I., Röckner, Michael, and Shaposhnikov, S. V. 2023. “Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes”. Theory of Probability and its Applications 68 (3): 342-369.
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2023 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2982418Albeverio, Sergio, Kawabi, Hiroshi, Ihalache, Stefan-Radu, and Röckner, Michael. 2023. “Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus”. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24 (1): 33-69.
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2023 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2978304Liu, Wei, Röckner, Michael, Sun, Xiaobin, and Xie, Yingchao. 2023. “Strong Averaging Principle for Slow-Fast Stochastic Partial Differential Equations with Locally Monotone Coefficients”. Applied Mathematics and Optimization 87 (3): 39.
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2022 | Zeitschriftenaufsatz | E-Veröff. vor dem Druck | PUB-ID: 2967252Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. 2022. “Zvonkin's transform and the regularity of solutions to double divergence form elliptic equations”. Communications in Partial Differential Equations .
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2022 | Zeitschriftenaufsatz | E-Veröff. vor dem Druck | PUB-ID: 2965241Banas, Lubomir, Röckner, Michael, and Wilke, Andre. 2022. “Correction to: Convergent numerical approximation of the stochastic total variation flow (vol 9, pg 437, 2021)”. Stochastics and Partial Differential Equations : Analysis and Computations .
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2022 | Diskussionspapier | Veröffentlicht | PUB-ID: 2962548Goldys, Ben, Nendel, Max, and Röckner, Michael. 2022. Operator Semigroups in the Mixed Topology and the Infinitesimal description of Markov Processes. Vol. 665. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
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2022 | Zeitschriftenaufsatz | E-Veröff. vor dem Druck | PUB-ID: 2962448Röckner, Michael, Xie, Longjie, and Yang, Li. 2022. “Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations”. Stochastics and Partial Differential Equations: Analysis and Computations .
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2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2960405Nendel, Max, and Röckner, Michael. 2021. “Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823”. SIAM Journal on Control and Optimization 59 (6): 4400-4428.
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2021 | Zeitschriftenaufsatz | E-Veröff. vor dem Druck | PUB-ID: 2959755Barbu, Viorel, and Röckner, Michael. 2021. “Correction to: Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs ”. Stochastics and Partial Differential Equations: Analysis and Computations .
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2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2957066Liu, Wei, Röckner, Michael, and da Silva, Jose Luis. 2021. “Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations”. Journal of Functional Analysis 281 (8): 109135.
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2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2956999Majid, Narges Rezvani, and Röckner, Michael. 2021. “The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 24 (02): 2150011.
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2021 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2953834Röckner, Michael, Sun, Xiaobin, and Xie, Yingchao. 2021. “Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations”. Annales de l'Institut Henri Poincaré (B): Probability and Statistics 57 (1): 547-576.
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2020 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2942720Banas, Lubomir, Röckner, Michael, and Wilke, Andre. 2020. “Convergent numerical approximation of the stochastic total variation flow”. Stochastics and Partial Differential Equations : Analysis and Computations 9 (2): 437-471.
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2020 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2948625Beznea, Lucian, Cimpean, Iulian, and Röckner, Michael. 2020. “A natural extension of Markov processes and applications to singular SDEs”. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56 (4): 2480-2506.
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2020 | Zeitschriftenaufsatz | E-Veröff. vor dem Druck | PUB-ID: 2946115Barbu, Viorel, and Röckner, Michael. 2020. “Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs”. Stochastics and Partial Differential Equations: Analysis and Computations .
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2020 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2943809Da Prato, Giuseppe, Flandoli, Franco, and Röckner, Michael. 2020. “Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure”. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS.
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2020 | Zeitschriftenaufsatz | E-Veröff. vor dem Druck | PUB-ID: 2941889Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. 2020. “On the Ambrosio-Figalli-Trevisan Superposition Principle for Probability Solutions to Fokker-Planck-Kolmogorov Equations”. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.
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2020 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2940088Liu, Wei, Röckner, Michael, Sun, Xiaobin, and Xie, Yingchao. 2020. “Averaging principle for slow-fast stochastic differential equations with time dependent locally Lipschitz coefficients”. JOURNAL OF DIFFERENTIAL EQUATIONS 268 (6): 2910-2948.
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2019 | Diskussionspapier | Veröffentlicht | PUB-ID: 2936013Nendel, Max, and Röckner, Michael. 2019. Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems. Vol. 618. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
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2019 | Diskussionspapier | Veröffentlicht | PUB-ID: 2935374Federico, Salvatore, Ferrari, Giorgio, Riedel, Frank, and Röckner, Michael. 2019. On a Class of Infinite-Dimensional Singular Stochastic Control Problems. Vol. 614. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
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2019 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2934374Huang, Xing, Röckner, Michael, and Wang, Feng-Yu. 2019. “Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs”. Discrete and Continuous Dynamical Systems 39 (6): 3017-3035.
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2019 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2935865Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. 2019. “Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures”. Journal of Functional Analysis 276 (12): 3681-3713.
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2019 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2936025Beznea, Lucian, Cimpean, Iulian, and Röckner, Michael. 2019. “A new approach to the existence of invariant measures for Markovian semigroups”. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 55 (2): 977-1000.
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2019 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2934350Herr, Sebastian, Röckner, Michael, and Zhang, Deng. 2019. “Scattering for stochastic nonlinear Schrödinger equations”. Communications in Mathematical Physics 368 (2): 843–884.
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2018 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2931102Barbu, Viorel, and Röckner, Michael. 2018. “Variational solutions to nonlinear stochastic differential equations in Hilbert spaces”. Stochastics and Partial Differential Equations: Analysis and Computations 6 (3): 500-524.
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2018 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2919064Grigoryan, Alexander, Ouyang, Shunxiang, and Röckner, Michael. 2018. “Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities”. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 736 (736): 1-31.
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2017 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2916350Barbu, Viorel, Röckner, Michael, and Russo, Francesco. 2017. “Doubly probabilistic representation for the stochastic porous media type equation”. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53 (4): 2043-2073.
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2017 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2916113Barbu, Viorel, and Röckner, Michael. 2017. “A splitting algorithm for stochastic partial differential equations driven by linear multiplicative noise”. Stochastics and Partial Differential Equations: Analysis and Computations 5 (4): 457-471.
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2017 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2910486Gess, Benjamin, and Röckner, Michael. 2017. “STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS”. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 369 (5): 3017-3045.
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2016 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2907737Röckner, Michael, Shin, Jiyong, and Trutnau, Gerald. 2016. “Non-symmetric distorted Brownian motion: Strong solutions, strong Feller property and non-explosion results”. Discrete and Continuous Dynamical Systems. Series B 21 (9): 3219-3237.
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911801Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “Transition Semigroup”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:167-195. Lecture Notes in Mathematics. Cham: Springer Int Publishing AG.
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911796Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “Equations with Lipschitz Nonlinearities”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:19-47. Lecture Notes in Mathematics. Cham: Springer .
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2016 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2905502Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. 2016. “Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations”. Journal of Functional Analysis 271 (5): 1262-1300.
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911797Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “Equations with Maximal Monotone Nonlinearities”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:49-93. Lecture Notes in Mathematics. Cham: Springer .
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911798Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “Variational Approach to Stochastic Porous Media Equations”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:95-106. Lecture Notes in Mathematics. Cham: Springer Int Publishing AG.
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911794Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “Stochastic Porous Media Equations Introduction”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:1-18. Lecture Notes in Mathematics. Cham: Springer Int Publishing AG.
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911800Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “The Stochastic Porous Media Equations in ℝ<sup>d</sup>”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:133-165. Lecture Notes in Mathematics. Cham: Springer Int Publishing AG.
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2016 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 2911799Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2016. “L-1-Based Approach to Existence Theory for Stochastic Porous Media Equations”. In Stochastic porous media equations, ed. Viorel Barbu, Giuseppe Da Prato, and Michael Röckner, 2163:107-131. Lecture Notes in Mathematics. Cham: Springer Int Publishing AG.
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2015 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2901228Bogachev, Vladimir I., Da Prato, Giuseppe, Röckner, Michael, and Shaposhnikov, Stanislav V. 2015. “An analytic approach to infinite-dimensional continuity and fokker-planck-kolmogorov equations”. Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze 14 (3): 983-1023.
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2015 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2772441Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. 2015. “Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions”. Nonlinear Analysis Theory Methods & Applications 125: 358-397.
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2014 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2677412Albeverio, Sergio, Röckner, Michael, and Yoshida, Minoru W. 2014. “A homeomorphism relating path spaces of stochastic processes with values in R-Z respectively (S-1)(Z)”. Infinite Dimensional Analysis Quantum Probability and Related Topics 17 (1): 1450002.
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2014 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2677363Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. 2014. “Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise”. Stochastic Processes and their Applications 124 (5): 1974-2002.
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2013 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2612709Barbu, Viorel, and Röckner, Michael. 2013. “Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise”. Archive For Rational Mechanics And Analysis 209 (3): 797-834.
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2013 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2625721Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. 2013. “On uniqueness of solutions to the Cauchy problem for degenerate Fokker-Planck-Kolmogorov equations”. Journal Of Evolution Equations 13 (3): 577-593.
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2013 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2635459Hinz, Michael, Röckner, Michael, and Teplyaev, Alexander. 2013. “Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces”. Stochastic Processes And Their Applications 123 (12): 4373-4406.
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2013 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2636018Da Prato, Giuseppe, Flandoli, F., Priola, E., and Röckner, Michael. 2013. “Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift”. The Annals Of Probability 41 (5): 3306-3344.
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2012 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2560367Da Prato, Giuseppe, and Röckner, Michael. 2012. “Well posedness of Fokker-Planck equations for generators of time-inhomogeneous Markovian transition probabilities”. Rendiconti Lincei - Matematica E Applicazioni 23 (4): 361-376.
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2012 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2493091Barbu, Viorel, Da Prato, Giuseppe, and Röckner, Michael. 2012. “Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise”. Journal of Mathematical Analysis and Applications 389 (1): 147-164.
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2011 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2454846Barbu, Viorel, Röckner, Michael, and Russo, Francesco. 2011. “Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case”. Probability Theory and Related Fields 151 (1-2): 1-43.
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2011 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2440773Beznea, Lucian, and Röckner, Michael. 2011. “From resolvents to cadlag processes through compact excessive functions and applications to singular SDE on Hilbert spaces”. Bulletin des Sciences Mathématiques 135 (6-7): 844-870.
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2011 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 2003388Beyn, Wolf-Jürgen, Gess, Benjamin, Lescot, Paul, and Röckner, Michael. 2011. “The Global Random Attractor for a Class of Stochastic Porous Media Equations”. Communications in Partial Differential Equations 36 (3): 446-469.
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2010 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1796081Röckner, Michael, and Wang, Feng-Yu. 2010. “LOG-HARNACK INEQUALITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES AND ITS CONSEQUENCES”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 13 (1): 27-37.
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2009 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1635704Bogachev, Vladimir I., Da Prato, Giuseppe, and Röckner, Michael. 2009. “Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces”. Journal of Functional Analysis 256 (4): 1269-1298.
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2008 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1636506Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, S. V. 2008. “Estimates of Densities of Stationary Distributions and Transition Probabilities of Diffusion Processes ”. Theory of Probability & Its Applications 52 (2): 209-236.
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2008 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1592122Beznea, Lucian, Boboc, Nicu, and Röckner, Michael. 2008. “Markov processes associated with L-P-resolvents, applications to quasi-regular Dirichlet forms and stochastic differential equations”. Comptes Rendus Mathematique 346 (5-6): 323-328.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794538Prévôt, Claudia, and Röckner, Michael. 2007. “Weak and Strong Solutions: the Yamada-Watanabe Theorem”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:121-132. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794526Prévôt, Claudia, and Röckner, Michael. 2007. “The Bochner Integral”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:105-108. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794520Prévôt, Claudia, and Röckner, Michael. 2007. “Stochastic Differential Equations in Finite Dimensions”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:43-54. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794532Prévôt, Claudia, and Röckner, Michael. 2007. “Pseudo Inverse of Linear Operators”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:115-117. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794529Prévôt, Claudia, and Röckner, Michael. 2007. “Nuclear and Hilbert-Schmidt Operators”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:109-113. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794535Prévôt, Claudia, and Röckner, Michael. 2007. “Some Tools from Real Martingale Theory”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:119-119. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794541Prévôt, Claudia, and Röckner, Michael. 2007. “Strong, Mild and Weak Solutions”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:133-136. Lecture Notes in Mathematics. Berlin: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794514Prévôt, Claudia, and Röckner, Michael. 2007. “Motivation, Aims and Examples”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:1-4. Lecture Notes in Mathematics. Berling: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794523Prévôt, Claudia, and Röckner, Michael. 2007. “A Class of Stochastic Differential Equations”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:55-103. Lecture Notes in Mathematics. Berlin ; Heidelberg: Springer.
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2007 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1794517Prévôt, Claudia, and Röckner, Michael. 2007. “The Stochastic Integral in General Hilbert Spaces (w.r.t. Brownian Motion)”. In A Concise Course on Stochastic Partial Differential Equations, ed. Claudia Prévôt and Michael Röckner, 1905:5-42. Lecture Notes in Mathematics. Berlin ; Heidelberg: Springer.
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2006 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1874564Röckner, Michael, and Sobol, Zeev. 2006. “Kolmogorov Equations in Infinite Dimensions: Well-Posedness, Regularity of Solutions, and Applications to Stochastic Generalized Burgers Equations”. The Annals of Probability 34 (2): 663-727.
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2006 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1872394Bogachev, Vladimir I., Da Prato, Giuseppe, Röckner, Michael, and Sobol, Zeev. 2006. “Gradient bounds for solutions of elliptic and parabolic equations”. In Stochastic Differential Equations and Applications - VII, ed. Giuseppe Da Prato and Luciano Tubaro, 245:27-34. Lecture notes in pure and applied mathematics. Boca Raton: Chapman & Hall/CRC.
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2006 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1596907Beznea, Lucian, Boboc, Nicu, and Röckner, Michael. 2006. “Markov processes associated with L-p-resolvents and applications to stochastic differential equations on Hilbert space”. Journal of Evolution Equations 6 (4): 745-772.
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2006 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1599008Barbu, Viorel, Bogachev, Vladimir I., Da Prato, Giuseppe, and Röckner, Michael. 2006. “Weak solutions to the stochastic porous media equation via Kolmogorov equations: The degenerate case”. Journal of Functional Analysis 237 (1): 54-75.
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2006 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1600893Da Prato, Giuseppe, Röckner, Michael, Rozovskii, B.L., and Wang, Feng-Yu. 2006. “Strong solutions of stochastic generalized porous media equations: Existence, uniqueness, and ergodicity”. Communications in Partial Differential Equations 31 (2): 277-291.
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2005 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1872405Bernabei, Simonetta, Röckner, Michael, Yoshida, MInoru W., and Albeverio, Sergio. 2005. “Homogenization with respect to Gibbs measures for periodic drift diffusions on lattices”. Comptes Rendus Mathematique 341 (11): 675-678.
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2005 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1872430Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. 2005. “Global regularity and bounds for solutions of parabolic equations for probability measures”. SIAM Theory of Probability and its Applications 50 (4): 561-581.
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2005 | Konferenzbeitrag | Veröffentlicht | PUB-ID: 1872422Ren, Jiagang, and Röckner, Michael. 2005. “A remark on sets in infinite dimensional spaces with full or zero capacity”. In Stochastic Analysis: Classical and Quantum. Perspectives of white noise theory., 177-186. Singapore: World Scientific.
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2005 | Konferenzbeitrag | Veröffentlicht | PUB-ID: 1874572Röckner, Michael. 2005. “PDE Approach to Invariant and Gibbs Measures with Applications”. In Infinite Dimensional Harmonic Analysis III, ed. Herbert Heyer, 3:351. Infinite dimensional harmonic analysis. Hackensack, N.J: World Scientific.
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2005 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1605081Cerrai, Sandra, and Röckner, Michael. 2005. “Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term”. Annales de l'Institut Henri Poincare (B) Probability and Statistics 41 (1): 69-105.
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2005 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1874610Albeverio, Sergio, Röckner, Michael, Pasurek, Tatiana, and Kondratiev, Yuri. 2005. “Euclidean Gibbs Measures of Quantum Crystals: Existence, Uniqueness and A-Priori Estimates”. In Interacting Stochastic Systems, ed. Jean-Dominique Deuschel, 29-54. Berlin: Springer.
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2004 | Konferenzbeitrag | Veröffentlicht | PUB-ID: 1877234Da Prato, Guiseppe, and Röckner, Michael. 2004. “Invariant Measures for a Stochastic Porous Medium Equation”. In Stochastic Analysis and Related Topics, ed. Hiroshi Kunita, Shinzo Watanabe, and Yoichiro Takahashi, 41:13-29. Advanced studies in pure mathematics. Tokyo: Mathematical Soc. of Japan.
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2004 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1606613Röckner, Michael, and Zhang, Tusheng S. 2004. “Sample path large deviations for diffusion processes on configuration spaces over a Riemannian manifold”. Publications of the Research Institute for Mathematical Sciences 40 (2): 385-427.
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2003 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1611843Albeverio, Sergio, Kondratiev, Yuri, Kozitsky, Yuri, and Röckner, Michael. 2003. “Quantum stabilization in anharmonic crystals”. PHYSICAL REVIEW LETTERS 90 (17): 170603.
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2001 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1615560Bogachev, VI, Krylov, NV, and Röckner, Michael. 2001. “On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions”. Communications in Partial Differential Equations 26 (11-12): 2037-2080.
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2001 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1617681Bogachev, Vladimir, Röckner, Michael, and Wang, Feng-Yu. 2001. “Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions”. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332 (4): 333-338.
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2001 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1615484Finkelshtein, DL, Kondratiev, Yuri, Röckner, Michael, and Konstantinov, AY. 2001. “Gauss formula and symmetric extensions of the Laplacian on configuration spaces”. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS 4 (4): 489-509.
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2001 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1615500Albeverio, Sergio, Kondratiev, Yuri, Pasurek, Tatiana, and Röckner, Michael. 2001. “Gibbs states on loop lattices: existence and a priori estimates”. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 333 (11): 1005-1009.
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2001 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1617918Albeverio, Sergio, Kondratiev, Yuri, Kozitsky, Yuri, and Röckner, Michael. 2001. “Uniqueness for Gibbs measures of quantum lattices in small mass regime”. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 37 (1): 43-69.
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2000 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1620414Albeverio, Sergio, Kondratiev, Yuri, Röckner, Michael, and Tsikalenko, Tatiana V. 2000. “A priori estimates for symmetrizing measures and their applications to Gibbs states”. JOURNAL OF FUNCTIONAL ANALYSIS 171 (2): 366-400.
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1999 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1620659Liskevich, Vitali, Sobol, Zeev, and Röckner, Michael. 1999. “Dirichlet operators with variable coefficients in L-p-spaces of functions of infinitely many variables coefficients”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 (4): 487-502.
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1999 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1621467Bogachev, Vladimir, and Röckner, Michael. 1999. “Elliptic equations for infinite dimensional probability distributions and Lyapunov functions”. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 329 (8): 705-710.
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1999 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1622749Albeverio, Sergio, Kondratiev, Yuri, Röckner, Michael, and Tsikalenko, Tatiana V. 1999. “A-priori estimates and existence of Gibbs measures: a simplified proof”. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 328 (11): 1049-1054.
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1998 | Sammelwerksbeitrag | Veröffentlicht | PUB-ID: 1884927Röckner, Michael. 1998. “Stochastic Analysis on Configuration Spaces: Basic Ideas and Recent Results”. In New Directions in Dirichlet Forms, ed. Jürgen Jost, 157-231. Studies in Advances Mathematics. Providence, RI: American Mathematical Society.
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1998 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1884916Liskevich, Vitali I., and Röckner, Michael. 1998. “Strong Uniqueness for a Class of Intinite Dimensional Dirichlet Operators and Applications to Stochastic Quantization”. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4 27 (1): 69-91.
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1996 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1628378Albeverio, Sergio, Kondratiev, Yuri, and Röckner, Michael. 1996. “Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces”. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 323 (11): 1179-1184.
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1991 | Zeitschriftenaufsatz | Veröffentlicht | PUB-ID: 1649910Albeverio, Sergio, FUKUSHIMA, M, Hansen, Wolfhard, MA, ZM, and Röckner, Michael. 1991. “CAPACITIES ON WIENER SPACE - TIGHTNESS AND INVARIANCE”. Comptes Rendus de l'Academie des Sciences. Series I, Mathematics 312 (12): 931-935.
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