Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations

Anthony Le Cavil (1, 2) , Nadia Oudjane (1, 3) , Francesco Russo (2, 4)

1 EDF R&D - EDF R&D
2 UMA - Unité de Mathématiques Appliquées
3 FiME Lab - Laboratoire de Finance des Marchés d'Energie
4 OC - Optimisation et commande

We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions.

Mots clés: Nonlinear McKean type Stochastic Differential Equations; Nonlinear Partial Differential Equations; Probabilistic representation of PDEs; Wasserstein type distance

Domaines: Probabilités [math.PR]

Anthony Le Cavil, Nadia Oudjane, Francesco Russo. Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations: About probabilistic representation of non-conservative PDEs.. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2016, 13, pp.1189-1233. ⟨10.30757/ALEA.v13-43⟩. ⟨hal-01241701v2⟩