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Stochastic Analysis: A Series of Lectures

Centre Interfacultaire Bernoulli, January–June 2012, Ecole Polytechnique Fédérale de Lausanne, Switzerland

  • Conference proceedings
  • © 2015

Overview

Editors:
  1. Robert C. Dalang

    1. Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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  2. Marco Dozzi

    1. Institut Elie Cartan, Université de Lorraine, Vandoeuvre-lès-Nancy, France

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  3. Franco Flandoli

    1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

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  4. Francesco Russo

    1. Unité de Mathématiques Appliquées, ENSTA ParisTech, Université Paris-Saclay, Palaiseau, France

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Part of the book series: Progress in Probability (PRPR, volume 68)

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Table of contents (13 papers)

  1. Front Matter

    Pages i-xiii
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  2. An Introduction to Infinite-dimensional Oscillatory and Probabilistic Integrals

    • Sergio Albeverio, Sonia Mazzucchi
    Pages 1-54

  3. Stochastic Lagrangian Flows and the Navier–Stokes Equations

    • Marc Arnaudon, Ana Bela Cruzeiro
    Pages 55-75

  4. Integration by Parts Formulas and Regularity of Probability Laws

    • Vlad Bally
    Pages 77-100

  5. Stochastic Porous Media Equations

    • Viorel Barbu
    Pages 101-133

  6. Stochastic Incompressible Euler Equations in a Two-dimensional Domain

    • Hakima Bessaih
    Pages 135-155

  7. Stochastic Geometric Wave Equations

    • Zdzisław Brzeźniak, Martin Ondreját
    Pages 157-188

  8. Reflections on Reflections

    • Krzysztof Burdzy
    Pages 189-220

  9. A Stochastic View over the Open Problem of Well-posedness for the 3D Navier–Stokes Equations

    • Franco Flandoli
    Pages 221-246

  10. A Short Course on Weak Approximations for Lévy Driven SDE’s

    • Arturo Kohatsu-Higa
    Pages 247-270

  11. Stochastic PDE from the Point of View of Particle Systems and Duality

    • Carl Mueller
    Pages 271-295

  12. Stochastic Integration in Banach Spaces – a Survey

    • Jan van Neerven, Mark Veraar, Lutz Weis
    Pages 297-332

  13. Stochastic Partial Differential Equations with Lévy Noise (a Few Aspects)

    • Szymon Peszat
    Pages 333-357

  14. The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)

    • Jean-Claude Zambrini
    Pages 359-393
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Keywords

About this book

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

Editors and Affiliations

  • Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Robert C. Dalang

  • Institut Elie Cartan, Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Marco Dozzi

  • Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Franco Flandoli

  • Unité de Mathématiques Appliquées, ENSTA ParisTech, Université Paris-Saclay, Palaiseau, France

    Francesco Russo

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