McKean Feynman-Kac probabilistic representations of non-linear partial differential equations
december, 2021
Publication type:
Paper in peer-reviewed journals
Journal:
Geometry and Invariance in Stochastic Dynamics. Eds. S. Ugolini et al., vol. 378, pp. 187-212
Publisher:
Springer
ISBN:
978-3-030-87432-2
HAL:
arXiv:
Keywords :
Backward diffusion; McKean stochastic differential equation; Probabilistic representation of PDEs; Time reversed diffusion; HJB equation; Feynman-Kac measures;
Abstract:
This paper presents a partial state of the art about the topic
of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs).
While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come
from modeling issues but also from numerical approximation issues
in computing the solution of a PDE, arising for instance in the context of stochastic control.
MFKEs also appear naturally in representing final value problems related to backward Fokker-Planck equations.
BibTeX:
@article{Izy-Oud-Rus-2021-1,
author={Lucas Izydorczyk and Nadia Oudjane and Francesco Russo },
title={McKean Feynman-Kac probabilistic representations of non-linear
partial differential equations },
doi={10.1007/978-3-030-87432-2 },
journal={Geometry and Invariance in Stochastic Dynamics. Eds. S.
Ugolini et al. },
year={2021 },
month={12},
volume={378 },
pages={187--212},
}