Abstract
In this paper, we present a local Lipchitz condition for the local existence of solution to a class of stochastic differential equations with finite delay in a real separable Hilbert space which has the following form:
Highlights
The purpose of this paper focuses on the local existence of mild solution to a class of the following stochastic differential equations with finite delay in a real separable Hilbert space H
Cr is the space of all continuous functions from, 0 into H equipped with the norm
We prove the local existence of solution for Equation (1) with the weaker condition on A, f ; and g
Summary
The purpose of this paper focuses on the local existence of mild solution to a class of the following stochastic differential equations with finite delay in a real separable Hilbert space H Cr is the space of all continuous functions from , 0 into H equipped with the norm In [1], if A is the generator of a uniformly exponentially stable semi-group in H ; f , g satisfies Lipchitz and linear growth conditions the mild solution of Equation (1) is exponentially stable in mean square. We prove the local existence of solution for Equation (1) with the weaker condition on A, f ; and g.
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