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1

Probabilistic Representation for Solutions to Nonlinear Fokker--Planck Equations

Barbu, Viorel, Röckner, Michael

Journal:

SIAM Journal on Mathematical Analysis

Year:

2018

Language:

english

File:

PDF, 336 KB

english, 2018

2

Ergodicity for the Stochastic Dynamics of Quasi-invariant Measures with Applications to Gibbs States

Sergio Albeverio, Yuri G. Kondratiev, Michael Röckner

Journal:

Journal of Functional Analysis

Year:

1997

Language:

english

File:

PDF, 621 KB

english, 1997

3

[Universitext] Introduction to the Theory of (Non-Symmetric) Dirichlet Forms ||

Ma, Zhi-Ming, Röckner, Michael

Year:

1992

Language:

english

File:

PDF, 27.02 MB

english, 1992

4

[Lecture Notes in Mathematics] Stochastic PDE’s and Kolmogorov Equations in Infinite Dimensions Volume 1715 || Parabolic equations on Hilbert spaces

Krylov, Nikolai A., Zabczyk, Jerzy, Röckner, Michael, Da Prato, Giueppe

Year:

1999

Language:

english

File:

PDF, 4.71 MB

english, 1999

5

[Universitext] Stochastic Partial Differential Equations: An Introduction || The Stochastic Integral in General Hilbert Spaces (w.r.t. Brownian Motion)

Liu, Wei, Röckner, Michael

Year:

2015

Language:

english

File:

PDF, 382 KB

english, 2015

6

Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise

Barbu, Viorel, Röckner, Michael, Zhang, Deng

Journal:

The Annals of Probability

Year:

2018

Language:

english

File:

PDF, 424 KB

english, 2018

7

Martingale solutions and Markov selections for stochastic partial differential equations

Benjamin Goldys, Michael Röckner, Xicheng Zhang

Journal:

Stochastic Processes and their Applications

Year:

2009

Language:

english

File:

PDF, 1.39 MB

english, 2009

8

[Lecture Notes in Mathematics] Dirichlet Forms Volume 1563 || Logarithmic Sobolev inequalities for gibbs states

Fabes, Eugene, Fukushima, Masatoshi, Gross, Leonard, Kenig, Carlos, Röckner, Michael, Stroock, Daniel W., Dell'Antonio, Gianfausto, Mosco, Umberto

Year:

1993

Language:

english

File:

PDF, 1.86 MB

english, 1993

9

Harnack Inequalities and Applications for Ornstein–Uhlenbeck Semigroups with Jump

Shun-Xiang Ouyang, Michael Röckner, Feng-Yu Wang

Journal:

Potential Analysis

Year:

2012

Language:

english

File:

PDF, 350 KB

english, 2012

10

Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise

Arnulf Jentzen, Michael Röckner

Journal:

Journal of Differential Equations

Year:

2012

Language:

english

File:

PDF, 286 KB

english, 2012

11

Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations

Gess, Benjamin, Röckner, Michael

Journal:

Transactions of the American Mathematical Society

Year:

2016

Language:

english

File:

PDF, 334 KB

english, 2016

12

Partitions of Unity in Sobolev Spaces over Infinite Dimensional State Spaces

S. Albeverio, Zhi-Ming Ma, Michael Röckner

Journal:

Journal of Functional Analysis

Year:

1997

Language:

english

File:

PDF, 2.19 MB

english, 1997

13

Regularity of Invariant Measures on Finite and Infinite Dimensional Spaces and Applications

V.I. Bogachev, M. Rockner

Journal:

Journal of Functional Analysis

Year:

1995

File:

PDF, 1.88 MB

1995

14

Harnack and functional inequalities for generalized Mehler semigroups

Michael Röckner, Feng-Yu Wang

Journal:

Journal of Functional Analysis

Year:

2003

Language:

english

File:

PDF, 277 KB

english, 2003

15

Traces of harmonic functions and a new path space for the free quantum field

Michael Röckner

Journal:

Journal of Functional Analysis

Year:

1988

Language:

english

File:

PDF, 1.82 MB

english, 1988

16

Analysis and Geometry on Configuration Spaces

S Albeverio, Yu.G Kondratiev, M Röckner

Journal:

Journal of Functional Analysis

Year:

1998

Language:

english

File:

PDF, 612 KB

english, 1998

17

Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise

Carlo Marinelli, Claudia Prévôt, Michael Röckner

Journal:

Journal of Functional Analysis

Year:

2010

Language:

english

File:

PDF, 292 KB

english, 2010

18

[Universitext] Stochastic Partial Differential Equations: An Introduction ||

Liu, Wei, Röckner, Michael

Year:

2015

Language:

english

File:

PDF, 2.07 MB

english, 2015

19

Strong solutions of stochastic equations with singular time dependent drift

N.V. Krylov, M. Röckner

Journal:

Probability Theory and Related Fields

Year:

2005

Language:

english

File:

PDF, 338 KB

english, 2005

20

Existence of Strong Solutions for Stochastic Porous Media Equation under General Monotonicity Conditions

Viorel Barbu, Giuseppe Da Prato and Michael Röckner

Journal:

The Annals of Probability

Year:

2009

Language:

english

File:

PDF, 1.34 MB

english, 2009

21

Weak Poincaré Inequalities and L2-Convergence Rates of Markov Semigroups

Michael Röckner, Feng-Yu Wang

Journal:

Journal of Functional Analysis

Year:

2001

Language:

english

File:

PDF, 293 KB

english, 2001

22

A Generalization of Khasminskii's Theorem on the Existence of Invariant Measures for Locally Integrable Drifts

Bogachev, V., Röckner, M.

Journal:

Theory of Probability & Its Applications

Year:

2001

Language:

english

File:

PDF, 216 KB

english, 2001

23

Analysis and Geometry on Configuration Spaces: The Gibbsian Case

S Albeverio, Yu.G Kondratiev, M Röckner

Journal:

Journal of Functional Analysis

Year:

1998

Language:

english

File:

PDF, 603 KB

english, 1998

24

A splitting algorithm for stochastic partial differential equations driven by linear multiplicative noise

Barbu, Viorel, Röckner, Michael

Journal:

Stochastic Partial Differential Equations: Analysis and Computations

Year:

2017

Language:

english

File:

PDF, 468 KB

english, 2017

25

[Lecture Notes in Mathematics] Stochastic PDE’s and Kolmogorov Equations in Infinite Dimensions Volume 1715 || On Kolmogorov’s equations for finite dimensional diffusions

Krylov, Nikolai A., Zabczyk, Jerzy, Röckner, Michael, Da Prato, Giueppe

Year:

1999

Language:

english

File:

PDF, 2.50 MB

english, 1999

26

Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions

Bogachev, V I, Rockner, M, Stannat, W

Journal:

Russian Academy of Sciences Sbornik Mathematics

Year:

2002

Language:

english

File:

PDF, 577 KB

english, 2002

27

Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift

Da Prato, G., Flandoli, F., Priola, E., Röckner, M.

Journal:

The Annals of Probability

Year:

2013

Language:

english

File:

PDF, 343 KB

english, 2013

28

A Priori Estimates for Symmetrizing Measures and Their Applications to Gibbs States

S. Albeverio, Yu.G. Kondratiev, M. Röckner, T.V. Tsikalenko

Journal:

Journal of Functional Analysis

Year:

2000

Language:

english

File:

PDF, 245 KB

english, 2000

29

Stochastic heat equations with values in a Riemannian manifold

Röckner, Michael, Wu, Bo, Zhu, Rongchan, Zhu, Xiangchan

Journal:

Rendiconti Lincei - Matematica e Applicazioni

Year:

2018

Language:

english

File:

PDF, 103 KB

english, 2018

30

General extinction results for stochastic partial differential equations and applications

Rockner, M., Wang, F.-Y.

Journal:

Journal of the London Mathematical Society

Year:

2013

Language:

english

File:

PDF, 275 KB

english, 2013

31

On continuity equations in infinite dimensions with non-Gaussian reference measure

Kolesnikov, Alexander V., Röckner, Michael

Journal:

Journal of Functional Analysis

Year:

2014

Language:

english

File:

PDF, 537 KB

english, 2014

32

Episiotomy and perineal trauma during childbirth

Gunny Röckner, Vivian Wahlberg, Anders Ölund

Journal:

Journal of Advanced Nursing

Year:

1989

Language:

english

File:

PDF, 372 KB

english, 1989

33

On the maximal inequalities of Burkholder, Davis and Gundy

Marinelli, Carlo, Röckner, Michael

Journal:

Expositiones Mathematicae

Year:

2015

Language:

english

File:

PDF, 393 KB

english, 2015

34

Quasi-regular Dirichlet Forms and Markov Processes

S. Albeverio, Z.M. Ma, M. Rockner

Journal:

Journal of Functional Analysis

Year:

1993

File:

PDF, 1.16 MB

1993

35

Dirichlet Operators via Stochastic Analysis

S. Albeverio, Y.G. Kondratiev, M. Rockner

Journal:

Journal of Functional Analysis

Year:

1995

File:

PDF, 1.19 MB

1995

36

Uniqueness of generalized Schrödinger operators and applications

Michael Röckner, Zhang Tu-Sheng

Journal:

Journal of Functional Analysis

Year:

1992

Language:

english

File:

PDF, 2.29 MB

english, 1992

37

Global gradient bounds for dissipative diffusion operators

Vladimir I. Bogachev, Giuseppe Da Prato, Michael Röckner, Zeev Sobol

Journal:

Comptes Rendus Mathematique

Year:

2004

File:

PDF, 122 KB

2004

38

Classical Dirichlet forms on topological vector spaces—Closability and a Cameron-Martin formula

Sergio Albeverio, Michael Röckner

Journal:

Journal of Functional Analysis

Year:

1990

Language:

english

File:

PDF, 2.23 MB

english, 1990

39

On Partial Integration in Infinite-Dimensional Space and Applications to Dirichlet Forms

Albeverio, S., Kusuoka, S., Rockner, M.

Journal:

Journal of the London Mathematical Society

Year:

1990

Language:

english

File:

PDF, 338 KB

english, 1990

40

Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness, and Ergodicity

Prato, G. Da, Röckner, Michael, Rozovskii, B. L., Wang, Feng-yu

Journal:

Communications in Partial Differential Equations

Year:

2006

Language:

english

File:

PDF, 166 KB

english, 2006

41

Large deviations for invariant measures of stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term

Sandra Cerrai, Michael Röckner

Journal:

Annales de l'Institut Henri Poincare (B) Probability and Statistics

Year:

2005

Language:

english

File:

PDF, 376 KB

english, 2005

42

Stochastic porous media equations in

Barbu, Viorel, Röckner, Michael, Russo, Francesco

Journal:

Journal de Mathématiques Pures et Appliquées

Year:

2015

Language:

english

File:

PDF, 516 KB

english, 2015

43

Markov property of generalized fields and axiomatic potential theory

Michael Röckner

Journal:

Mathematische Annalen

Year:

1983

Language:

english

File:

PDF, 1.04 MB

english, 1983

44

Fluctuations and Their Glauber Dynamics in Lattice Systems

Sergio Albeverio, Alexei Daletskii, Yuri Kondratiev, Michael Röckner

Journal:

Journal of Functional Analysis

Year:

1999

Language:

english

File:

PDF, 173 KB

english, 1999

45

Stochastic Evolution Equations of Jump Type: Existence, Uniqueness and Large Deviation Principles

Michael Röckner, Tusheng Zhang

Journal:

Potential Analysis

Year:

2007

Language:

english

File:

PDF, 449 KB

english, 2007

46

Characterization of (non-symmetric) semi-Dirichlet forms associated with Hunt processes

ALBEVERIO, S., MA, Z. M., RÖCKNER, M.

Journal:

Random Operators and Stochastic Equations

Year:

1995

File:

PDF, 31 KB

1995

47

A Milstein Scheme for SPDEs

Jentzen, Arnulf, Röckner, Michael

Journal:

Foundations of Computational Mathematics

Year:

2015

Language:

english

File:

PDF, 1008 KB

english, 2015

48

Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations

Bogachev, V.I., Röckner, M., Shaposhnikov, S.V.

Journal:

Journal of Functional Analysis

Year:

2016

Language:

english

File:

PDF, 1.82 MB

english, 2016

49

Stochastic Dynamics of Fluctuations in Classical Continuous Systems

Sergio Albeverio, Martin Grothaus, Yuri G. Kondratiev, Michael Röckner

Journal:

Journal of Functional Analysis

Year:

2001

Language:

english

File:

PDF, 205 KB

english, 2001

50

Uniqueness Problems for Degenerate Fokker–Planck–Kolmogorov Equations

Bogachev, V. I., Röckner, M., Shaposhnikov, S. V.

Journal:

Journal of Mathematical Sciences

Year:

2015

Language:

english

File:

PDF, 256 KB

english, 2015

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