Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations.

Anthony Le Cavil, Nadia Oudjane and Francesco Russo
august, 2016
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastics and partial differential equations: Analysis and Computation., pp. 1-37
Publisher:
Springer-Verlag
arXiv:
images/icons/icon_arxiv.png 1608.00832
Keywords :
Chaos propagation; Nonlinear Partial Differential Equations; McKean type Nonlinear Stochastic Differential Equations; Particle systems; Probabilistic representation of PDEs.
Abstract:
We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE.
BibTeX:
@article{LeC-Oud-Rus-2016-1,
    author={Anthony Le Cavil and Nadia Oudjane and Francesco Russo },
    title={Particle system algorithm and chaos propagation related to 
           non-conservative McKean type stochastic differential 
           equations. },
    doi={10.1007/s40072-016-0079-9 },
    journal={Stochastics and partial differential equations: Analysis and 
           Computation. },
    year={2016 },
    month={8},
    pages={1--37},
}