Stochastic Analysis: A Series of Lectures: Centre Interfacultaire Bernoulli, January–June 2012, Ecole Polytechnique Fédérale de Lausanne, Switzerland (Progress in Probability Book 68)

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 Lévy 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. Brzeźniak 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 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 Lévy 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. Brzeźniak 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 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 L©♭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 F©♭d©♭rale 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. Brze¿ðniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondrej©Łt S. Peszat M. Veraar L. Weis J.-C. Zambrini 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 Lévy Noise (a Few Aspects)....Pages 333-357 The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)....Pages 359-393 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 Federale de Lausanne, Switzerland, from January to June 2012.