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.

Keywords

• unbounded operator
• monotonicity
• q-wiener process
• semigroup
• approximation