Fokker-Planck equations with terminal condition and related McKean probabilistic representation
january, 2022
Publication type:
Paper in peer-reviewed journals
Journal:
Nonlinear Differential Equations and Applications NoDEA
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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}, }