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
arXiv:
images/icons/icon_arxiv.png 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. },
    journal={ALEA (Latin American Journal Of Probability And Mathematical 
           Statistics) },
    year={2016 },
    month={11},
    volume={13 },
    pages={1189–1233},
}