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Doklady Mathematics

, Volume 98, Issue 2, pp 475–479 | Cite as

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

  • V. I. Bogachev
  • T. I. Krasovitskii
  • S. V. Shaposhnikov
Mathematics
  • 3 Downloads

Abstract

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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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. I. Bogachev
    • 1
    • 2
    • 3
  • T. I. Krasovitskii
    • 1
  • S. V. Shaposhnikov
    • 1
    • 2
    • 3
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.St.-Tikhon’s Orthodox UniversityMoscowRussia

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