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Matematicheskie Zametki, 2024, Volume 116, Issue 3, paper published in the English version journal (Mi mzm14489)  

Papers published in the English version of the journal

On dependence of solutions to Fokker–Planck–Kolmogorov equations on their coefficients and initial data

V. I. Bogachevabcd, I. I. Malofeevbd, S. V. Shaposhnikovabc

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b National Research University Higher School of Economics, Moscow
c Moscow Center for Fundamental and Applied Mathematics
d St. Tikhon's Orthodox University, Moscow
Abstract: We consider the Cauchy problem for the Fokker–Planck–Kolmogorov equation where the coefficients and the initial data depend measurably on a parameter and show that there is a selection of a solution measurable with respect to the parameter. In particular, the coefficients and the initial data themselves can be regarded as parameters. Several settings of the problem are discussed in which the measurability of solutions with respect to parameters is established.
Keywords: Fokker–Planck–Kolmogorov equation, Cauchy problem, measurability with respect to a parameter.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
HSE Basic Research Program
The work of the first and third authors (presented in Secs. 2 and 3 was accomplished with the support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2022-284, The work of the second author (presented in Sec. 4) was conducted within the framework of the HSE University Basic Research Program.
Received: 07.08.2024
Revised: 07.08.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 3, Pages 421–431
DOI: https://doi.org/10.1134/S0001434624090037
Document Type: Article
Language: English
Citation: V. I. Bogachev, I. I. Malofeev, S. V. Shaposhnikov, “On dependence of solutions to Fokker–Planck–Kolmogorov equations on their coefficients and initial data”, Math. Notes, 116:3 (2024), 421–431
Citation in format AMSBIB
\Bibitem{BogMalSha24}
\by V.~I.~Bogachev, I.~I.~Malofeev, S.~V.~Shaposhnikov
\paper On dependence of solutions to Fokker--Planck--Kolmogorov equations on their coefficients and initial data
\jour Math. Notes
\yr 2024
\vol 116
\issue 3
\pages 421--431
\mathnet{http://mi.mathnet.ru/mzm14489}
\crossref{https://doi.org/10.1134/S0001434624090037}
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