Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations.
march, 2017
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastics and partial differential equations: Analysis and Computation., vol. 5 (1), pp. 1-37
Publisher:
Springer-Verlag
HAL:
arXiv:
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-2017,
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={2017 },
month={3},
volume={5 (1) },
pages={1--37},
}