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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