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Journal Articles Nonlinear Differential Equations and Applications Year : 2022

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

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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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Dates and versions

hal-02902615 , version 1 (20-07-2020)
hal-02902615 , version 2 (22-07-2020)
hal-02902615 , version 3 (27-09-2021)

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Lucas Izydorczyk, Nadia Oudjane, Francesco Russo, Gianmario Tessitore. Fokker-Planck equations with terminal condition and related McKean probabilistic representation. Nonlinear Differential Equations and Applications, 2022, volume 29 (10), ⟨10.1007/s00030-021-00736-1⟩. ⟨hal-02902615v3⟩
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