On Weak and Strong Solutions of Paired Stochastic Functional Differential Equations in Infinite-Dimensional Spaces

Abstract

In this paper, we study the questions of the existence of global weak solutions and local strong solutions of paired stochastic functional differential equations in a Hilbert space, one of which is an equation with an unbounded operator, and the other is an ordinary differential equation. We proved the existence and uniqueness theorems in the case of coefficients with polynomial growth.

On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations

“…Regarding stochastic functionaldifferential equations in infinite-dimensional spaces, the monograph [4] is noteworthy. The existence of invariant measures in shift spaces for stochastic functionaldifferential equations with partial derivatives is addressed in works [5][6][7][8]. In this work, the asymptotic behavior of solutions at infinity is investigated using a wellknown method in the theory of differential equations called the method of asymptotic equivalence.…”