Fokker-Planck equations with terminal condition and related McKean probabilistic representation

Lucas Izydorczyk, Nadia Oudjane, Francesco Russo and
Gianmario Tessitore

january, 2022

Publication type:

Paper in peer-reviewed journals

Journal:

Nonlinear Differential Equations and Applications NoDEA

DOI:

10.1007/s00030-021-00736-1

HAL:

hal-02902615

arXiv:

2007.10628

Keywords :

Inverse problem; McKean stochastic differential equation; probabilistic representation of PDEs; time-reversed diffusion; Fokker Planck equation.

Abstract:

Usually Fokker-Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we give sufficient conditions for existence and uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.

BibTeX:

@article{Izy-Oud-Rus-Tes-2022,
    author={Lucas Izydorczyk and Nadia Oudjane and Francesco Russo and 
           Gianmario Tessitore },
    title={Fokker-Planck equations with terminal condition and related 
           McKean probabilistic representation },
    doi={10.1007/s00030-021-00736-1 },
    journal={Nonlinear Differential Equations and Applications NoDEA },
    year={2022 },
    month={1},
}