论文标题
具有终端条件和相关McKean概率表示的Fokker-Planck方程
Fokker-Planck equations with terminal condition and related McKean probabilistic representation
论文作者
论文摘要
通常，如果指定初始条件，则通常可以很好地使用Fokker-Planck类型部分微分方程（PDE）。或者，在本文中，我们考虑了规定最终数据的逆问题：特别是我们为存在和独特性提供了足够的条件。在本文的第二部分中，我们在形式中提供了这些PDE的概率表示，以对应于扩散过程的时间反转动力学的麦基类型方程的解决方案。
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.
