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Probabilistic Models for Nonlinear Partial Differential Equations

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22-30, 1995

  • Book
  • © 1996

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Authors:
  1. Carl Graham
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  2. Thomas G. Kurtz
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  3. Sylvie Méléard
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  4. Philip E. Protter
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  5. Mario Pulvirenti
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  6. Denis Talay
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Editors:
  1. Denis Talay
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  2. Luciano Tubaro
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1627)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-X
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  2. Weak convergence of stochastic integrals and differential equations

    • Thomas G. Kurtz, Philip E. Protter
    Pages 1-41

  3. Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models

    • Sylvie Méléard
    Pages 42-95

  4. Kinetic limits for stochastic particle systems

    • Mario Pulvirenti
    Pages 96-126

  5. A statistical physics approach to large networks

    • Carl Graham
    Pages 127-147

  6. Probabilistic numerical methods for partial differential equations: Elements of analysis

    • Denis Talay
    Pages 148-196

  7. Weak convergence of stochastic integrals and differential equations II: Infinite dimensional case

    • Thomas G. Kurtz, Philip E. Protter
    Pages 197-285

  8. Back Matter

    Pages 287-302
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Keywords

About this book

The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems. This book, collecting the notes of these courses, will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.

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