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1. Stochastic Porous Media Equations
by Viorel Barbu, Giuseppe Da Prato, Michael Röckner
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2163
オンライン: http://dx.doi.org/10.1007/978-3-319-41069-2
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Foreword
Preface
Introduction
Equations with Lipschitz nonlinearities
Equations with maximal monotone nonlinearities
Variational approach to stochastic porous media equations
L1-based approach to existence theory for stochastic porous media equations
The stochastic porous media equations in Rd
Transition semigroups and ergodicity of invariant measures
Kolmogorov equations
A Two analytical inequalities
Bibliography
Glossary
Translator’s note
Index
Foreword
Preface
Introduction
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2. Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
by Raphael Kruse
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2093
オンライン: http://dx.doi.org/10.1007/978-3-319-02231-4
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Introduction
Stochastic Evolution Equations in Hilbert Spaces
Optimal Strong Error Estimates for Galerkin Finite Element Methods
A Short Review of the Malliavin Calculus in Hilbert Spaces
A Malliavin Calculus Approach to Weak Convergence
Numerical Experiments
Some Useful Variations of Gronwall’s Lemma
Results on Semigroups and their Infinitesimal Generators
A Generalized Version of Lebesgue’s Theorem
References
Index
Introduction
Stochastic Evolution Equations in Hilbert Spaces
Optimal Strong Error Estimates for Galerkin Finite Element Methods
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3. Brownian Motion and its Applications to Mathematical Analysis : École d'Été de Probabilités de Saint-Flour XLIII – 2013
by Krzysztof Burdzy
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2106
オンライン: http://dx.doi.org/10.1007/978-3-319-04394-4
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1. Brownian motion
2. Probabilistic proofs of classical theorems
3. Overview of the "hot spots" problem
4. Neumann eigenfunctions and eigenvalues
5. Synchronous and mirror couplings
6. Parabolic boundary Harnack principle
7. Scaling coupling
8. Nodal lines
9. Neumann heat kernel monotonicity
10. Reflected Brownian motion in time dependent domains
1. Brownian motion
2. Probabilistic proofs of classical theorems
3. Overview of the "hot spots" problem
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4. The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
by Arnaud Debussche, Michael Högele, Peter Imkeller
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2085
オンライン: http://dx.doi.org/10.1007/978-3-319-00828-8
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Introduction
The fine dynamics of the Chafee- Infante equation
The stochastic Chafee- Infante equation
The small deviation of the small noise solution
Asymptotic exit times
Asymptotic transition times
Localization and metastability
The source of stochastic models in conceptual climate dynamics
Introduction
The fine dynamics of the Chafee- Infante equation
The stochastic Chafee- Infante equation
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5. A Minicourse on Stochastic Partial Differential Equations
by Robert Dalang, Davar Khoshnevisan, Carl Mueller, David Nualart, Yimin Xiao ; edited by J. -M. Morel, F. Takens, B. Teissier, Davar Khoshnevisan, Firas Rassoul-Agha
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009
シリーズ名: Lecture Notes in Mathematics ; 1962
オンライン: http://dx.doi.org/10.1007/978-3-540-85994-9
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6. Boundary Value Problems and Markov Processes
by Kazuaki Taira
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2009
シリーズ名: Lecture Notes in Mathematics ; 1499
オンライン: http://dx.doi.org/10.1007/978-3-642-01677-6
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7. Entropy Methods for the Boltzmann Equation : Lectures from a Special Semester at the Centre Emile Borel, Institut H. Poincare, Paris, 2001
by Fraydoun Rezakhanlou, Cedric Villani ; edited by Francois Golse, Stefano Olla
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008
シリーズ名: Lecture Notes in Mathematics ; 1916
オンライン: http://dx.doi.org/10.1007/978-3-540-73705-6
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8. Multiscale Problems in the Life Sciences : From Microscopic to Macroscopic
by Jacek Banasiak, Mark A. J. Chaplain, Jacek Mikisz ; edited by Vincenzo Capasso, Miroslaw Lachowicz
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008
シリーズ名: Lecture Notes in Mathematics ; 1940
オンライン: http://dx.doi.org/10.1007/978-3-540-78362-6
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9. SPDE in Hydrodynamic: Recent Progress and Prospects : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy August 29-September 3, 2005
by Sergio Albeverio, Franco Flandoli, Yakov G. Sinai ; edited by Giuseppe Prato, Michael Ruckner
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008
シリーズ名: Lecture Notes in Mathematics ; 1942
オンライン: http://dx.doi.org/10.1007/978-3-540-78493-7
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10. A Concise Course on Stochastic Partial Differential Equations
by Claudia Prevot, Michael Rockner
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2007
シリーズ名: Lecture Notes in Mathematics ; 1905
オンライン: http://dx.doi.org/10.1007/978-3-540-70781-3
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