McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

Lucas Izydorczyk, Nadia Oudjane and Francesco Russo
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
arXiv:
assets/images/icons/icon_arxiv.png 1912.03146
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,
    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},
}