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.
Keywords:Fokker–Planck–Kolmogorov equation, Cauchy problem, uniqueness of a probability solution.
UDC:517.955
Presented:A. N. Shiryaev Received: 26.03.2021 Revised: 26.03.2021 Accepted: 04.04.2021