Existence, Global Attracting Sets and Exponential Decay of Solution to Stochastic Functional Integro-Differential Equations Driven by Rosenblatt Process Mahamat Hamit Mahamat Hassan, Mamadou Abdoul Diop, Ramkumar Kasinathan, Ravikumar Kasinathan

In this paper, we investigate a class of neutral stochastic functional integro-differential equations driven by Rosenblatt process in a Hilbert space. First, the existence and uniqueness of mild solution of an stochastic system driven by Rosenblatt process is established by combining some stochastic analysis techniques, resolvent operator theory, and stochastic integral inequalities. Further, the exponential decay in the p-th moment of the mild solution of the considered equations is investigated and the global attracting sets are identified. Finally, to illustrate our theoretical results an example is given.