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 uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form of a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.
Izydorczyk, L., Oudjane, N., Russo, F., Tessitore, G. (2022). Fokker–Planck equations with terminal condition and related McKean probabilistic representation. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 29(1) [10.1007/s00030-021-00736-1].
Fokker–Planck equations with terminal condition and related McKean probabilistic representation
Tessitore G.
2022
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 uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form of a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.
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