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ЖУРНАЛЫ // Математические заметки // Архив

Матем. заметки, 2024, том 116, выпуск 3, страницы 421–431 (Mi mzm14489)

Статьи, опубликованные в английской версии журнала

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

Аннотация: 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.

Ключевые слова: Fokker–Planck–Kolmogorov equation, Cauchy problem, measurability with respect to a parameter.

Поступило: 07.08.2024
Исправленный вариант: 07.08.2024

Язык публикации: английский


 Англоязычная версия: Mathematical Notes, 2024, 116:3, 421–431


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