On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations

Abstract

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.

Keywords

• asymptotic behavior
• delay
• cauchy matrix
• probability