On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations

This paper studies the asymptotic behavior of solutions of linear stochastic functional-differential equations. This behavior is investigated using the method of asymptotic equivalence, according to which an ordinary system of linear differential equations is constructed based on the initial stochastic system, and the asymptotic behavior of the solutions of this system is analogous to the behavior of the solutions of the initial system

On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations

This paper studies the asymptotic behavior of solutions of linear stochastic functional-differential equations. This behavior is investigated using the method of asymptotic equivalence, according to which an ordinary system of linear differential equations is constructed based on the initial stochastic system, and the asymptotic behavior of the solutions of this system is analogous to the behavior of the solutions of the initial system

Професор Г.Л. Кулініч (09.12.1938 – 10.02.2022) – видатний вчений і педагог

Pages of the article in the issue: 11 - 21 Language of the article: UkrainianСторінки у випуску: 11 - 21 Мова статті: українськ

Stochastic dynamic equations on general time scales

In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales Lebesgue integral and the Lebesgue integral in the common sense