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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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 et 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. 2020. ⟨hal-02902615v2⟩
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