On Almost Periodic Stochastic Difference Equations

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Abstract

In this paper almost periodic random sequence in mean is defined and investigated. It is then applied to study the existence and uniqueness of the almost periodic solution of a semi-linear system of stochastic difference equations of the form: $$\displaystyle\begin{array}{rcl} X(n + 1) = A(n)X(n) + f(n,X(n)),\,n \in \mathbb{Z}_{+}\,,& & \\ \end{array}$$ by means of exponential dichotomy.