Vol. 7(2) July 2019, No. 24, pp. 267-283.

GLOBAL ATTRACTING SET AND STABILITY FOR STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS
Vol. 7(2) July 2019, No. 24, pp. 267-283
DIEM DANG HUAN

Abstract

This article is concerned with existence, global attracting set and stability of mild solutions for a class of neutral stochastic integro-differential equations. The partial differential equations (PDEs) are driven by a fractional Brownian motion with Hurst index H ∈ ( 1 2 , 1) in Hilbert spaces. Existence theorems are proved via Banach fixed point theorem and resolvent operator theory for integro-differential equations. The global attracting set is obtained by integral inequalities. In addition, sufficient conditions for exponentially stability in mean square of the mild solution are presented.


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