On the existence of almost automorphic solutions of nonlinear stochastic Volterra difference equations. (English) Zbl 1274.39004

Summary: In this paper, we introduce a concept of almost automorphy for random sequences. Using the Banach contraction principle, we establish the existence and uniqueness of an almost automorphic solution to some Volterra stochastic difference equation in a Banach space. Our main results extend some known ones in the sense of mean almost automorphy. As an application, almost automorphic solution to a concrete stochastic difference equation is analyzed to illustrate our abstract results.


39A10 Additive difference equations
60G07 General theory of stochastic processes
34F05 Ordinary differential equations and systems with randomness
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