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

Anthony Le Cavil, Nadia Oudjane and Francesco Russo

november, 2016

Publication type:

Paper in peer-reviewed journals

Journal:

ALEA (Latin American Journal Of Probability And Mathematical Statistics), vol. 13, pp. 1189–1233

DOI:

10.30757/ALEA.v13-43

HAL:

hal-01241701

arXiv:

1504.03882

Keywords :

Nonlinear Partial Differential Equations; Nonlinear McKean type Stochastic Differential Equations; Particle systems; Probabilistic representation of PDEs; Wasserstein type distance.

Abstract:

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.

BibTeX:

@article{LeC-Oud-Rus-2016,
    author={Anthony Le Cavil and Nadia Oudjane and Francesco Russo },
    title={Probabilistic representation of a class of non conservative 
           nonlinear Partial Differential Equations. },
    doi={10.30757/ALEA.v13-43 },
    journal={ALEA (Latin American Journal Of Probability And Mathematical 
           Statistics) },
    year={2016 },
    month={11},
    volume={13 },
    pages={1189–1233},
}