Probabilistic Models for Nonlinear Partial Differential Equations [electronic resource] : 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 / by Carl Graham, Thomas G. Kurtz, Sylvie Mรฉlรฉard, Philip E. Protter, Mario Pulvirenti, Denis Talay ; edited by Denis Talay, Luciano Tubaro
Imprint
Berlin, Heidelberg : Springer Berlin Heidelberg, 1996
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
CONTENT
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
Mathematics
Partial differential equations
Numerical analysis
Probabilities
Thermodynamics
Statistical physics
Dynamical systems
Mathematics
Probability Theory and Stochastic Processes
Partial Differential Equations
Numerical Analysis
Thermodynamics
Statistical Physics Dynamical Systems and Complexity
