Email this article On Non-Uniqueness of Probability Solutions to the Two-Dimensional Stationary Fokker–Planck–Kolmogorov Equation
- Authors: Bogachev V.I.1,2,3, Krasovitskii T.I.1, Shaposhnikov S.V.1,2,3
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Affiliations:
- Department of Mechanics and Mathematics
- National Research University Higher School of Economics
- St.-Tikhon’s Orthodox University
- Issue: Vol 98, No 2 (2018)
- Pages: 475-479
- Section: Mathematics
- URL: https://journal-vniispk.ru/1064-5624/article/view/225561
- DOI: https://doi.org/10.1134/S1064562418060212
- ID: 225561
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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.
About the authors
V. I. Bogachev
Department of Mechanics and Mathematics; National Research University Higher School of Economics; St.-Tikhon’s Orthodox University
Author for correspondence.
Email: vibogach@mail.ru
Russian Federation, Moscow, 119991; Moscow; Moscow
T. I. Krasovitskii
Department of Mechanics and Mathematics
Email: vibogach@mail.ru
Russian Federation, Moscow, 119991
S. V. Shaposhnikov
Department of Mechanics and Mathematics; National Research University Higher School of Economics; St.-Tikhon’s Orthodox University
Email: vibogach@mail.ru
Russian Federation, Moscow, 119991; Moscow; Moscow
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