On Non-Uniqueness of Probability Solutions to the Two-Dimensional Stationary Fokker–Planck–Kolmogorov Equation


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The problem of uniqueness of probability solutions to the two-dimensional stationary Fokker–Planck–Kolmogorov equation is considered. Under broad conditions, it is proved that the existence of two different probability solutions implies the existence of an infinite set of linearly independent probability solutions.

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V. Bogachev

Department of Mechanics and Mathematics; National Research University Higher School of Economics; St.-Tikhon’s Orthodox University

编辑信件的主要联系方式.
Email: vibogach@mail.ru
俄罗斯联邦, Moscow, 119991; Moscow; Moscow

T. Krasovitskii

Department of Mechanics and Mathematics

Email: vibogach@mail.ru
俄罗斯联邦, Moscow, 119991

S. Shaposhnikov

Department of Mechanics and Mathematics; National Research University Higher School of Economics; St.-Tikhon’s Orthodox University

Email: vibogach@mail.ru
俄罗斯联邦, Moscow, 119991; Moscow; Moscow

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