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arXiv · 2007.10628

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

Lucas Izydorczyk·Nadia Oudjane·Francesco Russo·Gianmario Tessitore
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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.

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Lucas Izydorczyk, Nadia Oudjane, Francesco Russo, Gianmario Tessitore. 2020-07-21. Fokker-Planck equations with terminal condition and related McKean probabilistic representation. https://arxiv.org/abs/2007.10628

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