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

2020/07/21 by Lucas Izydorczyk, Nadia Oudjane, Izydorczyk, Lucas +5
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Gas Dynamics and Kinetic Theory #Probability (math.PR) #Statistical Mechanics and Entropy

paper · doi:10.48550/arxiv.2007.10628

openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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