Abstract

In this paper we give a positive answer to the question about the possibility of existence of several probability solutions to the Fokker–Planck–Kolmogorov equation for all initial conditions: we construct the first example of an equation with a unit diffusion matrix and a smooth drift coefficient for which the Cauchy problem with every probability initial condition has an infinite-dimensiona1 simplex of probability solutions.

中文翻译：

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福克-普朗克-柯尔莫哥洛夫方程柯西问题概率解的非唯一性

摘要

在本文中，我们对所有初始条件下 Fokker-Planck-Kolmogorov 方程存在多个概率解的可能性的问题给出了肯定的答案：我们构造了具有单位扩散矩阵和平滑漂移的方程的第一个例子具有每个概率初始条件的柯西问题都具有概率解的无限维单纯形的系数。