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Stochastic Analysis: A Series of Lectures: Centre Interfacultaire Bernoulli, January–June 2012, Ecole Polytechnique Fédérale de Lausanne, Switzerland

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This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or LĂ©vy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection.

The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics.

Contributors:

S. Albeverio
M. Arnaudon
V. Bally
V. Barbu
H. Bessaih
Z. BrzeĹşniak
K. Burdzy
A.B. Cruzeiro
F. Flandoli
A. Kohatsu-Higa
S. Mazzucchi
C. Mueller
J. van Neerven
M. Ondreját
S. Peszat
M. Veraar
L. Weis
J.-C. Zambrini

Author(s): Robert C. Dalang, Marco Dozzi, Franco Flandoli, Francesco Russo (eds.)
Series: Progress in Probability 68
Edition: 1
Publisher: Birkhäuser Basel
Year: 2015

Language: English
Pages: XIII, 393
Tags: Probability Theory and Stochastic Processes; Partial Differential Equations; Applications of Mathematics

Front Matter....Pages i-xiii
An Introduction to Infinite-dimensional Oscillatory and Probabilistic Integrals....Pages 1-54
Stochastic Lagrangian Flows and the Navier–Stokes Equations....Pages 55-75
Integration by Parts Formulas and Regularity of Probability Laws....Pages 77-100
Stochastic Porous Media Equations....Pages 101-133
Stochastic Incompressible Euler Equations in a Two-dimensional Domain....Pages 135-155
Stochastic Geometric Wave Equations....Pages 157-188
Reflections on Reflections....Pages 189-220
A Stochastic View over the Open Problem of Well-posedness for the 3D Navier–Stokes Equations....Pages 221-246
A Short Course on Weak Approximations for Lévy Driven SDE’s....Pages 247-270
Stochastic PDE from the Point of View of Particle Systems and Duality....Pages 271-295
Stochastic Integration in Banach Spaces – a Survey....Pages 297-332
Stochastic Partial Differential Equations with LĂ©vy Noise (a Few Aspects)....Pages 333-357
The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)....Pages 359-393