Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations.
april, 2014
Type de publication :
Cours
Journal :
Arxiv, HAL-ENSTA
HAL :
arXiv :
Mots clés :
Chaos propagation; Nonlinear Partial Differential Equations; Nonlinear Stochastic Differential Equations; Particle systems; Probabilistic representation of
PDEs; McKean-Vlasov
Résumé :
We introduce a new class of nonlinear Stochastic Differential Equations
in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDE). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system
for which we discuss the propagation of chaos.
To this system, we associate a random function which is proved to converge
to a solution of a regularized version of PDE.
BibTeX :
@misc{LeC-Oud-Rus-2014,
title={Probabilistic representation of a class of non conservative
nonlinear Partial Differential Equations. },
journal={Arxiv, HAL-ENSTA },
year={2014 },
month={4},
comment={{umatype:'cours'}},
}