Affiliations: [a] School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi 710071, China. E-mail: [email protected] | [b] Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, M.D. 21251, USA. E-mail: gaston.n’[email protected] | [c] School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China. E-mail: [email protected]
Abstract: In this paper, we consider recurrence of bounded solutions to semilinear stochastic integro-differential equations via uniformly exponentially stable resolvent operators family. Concretely, we first establish the existence and uniqueness of the L2-bounded solution to a semilinear stochastic integro-differential equations driven by Lévy processes, and then we show this kind of L2-bounded solution is almost automorphic in distribution or weighted pseudo almost automorphic in distribution under suitable conditions respectively.
Keywords: Stochastic integro-differential equations, almost automorphy in distribution, weighted pseudo almost automorphy in distribution, Lévy noise
