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.

Inhalt

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