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 / Edition 1

by Carl Graham, Denis Talay, Thomas G. Kurtz, Luciano Tubaro, Sylvie Meleard

Overview

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 shastic 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 shastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.

Product Details

ISBN-13:	9783540613978
Publisher:	Springer Berlin Heidelberg
Publication date:	08/16/1996
Series:	Lecture Notes in Mathematics , #1627
Edition description:	1996
Pages:	302
Product dimensions:	8.50(w) x 10.98(h) x 0.36(d)

Table of Contents

Weak convergence of shastic integrals and differential equations.- Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models.- Kinetic limits for shastic particle systems.- A statistical physics approach to large networks.- Probabilistic numerical methods for partial differential equations: Elements of analysis.- Weak convergence of shastic integrals and differential equations II: Infinite dimensional case.