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Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. (English) Zbl 1043.60513
Summary: We associate in a canonical way to an almost periodic affine SDE a stochastic equation driven by a dynamical system. We prove the existence of a unique stationary solution provided the corresponding linear SDE is hyperbolic. If the linear SDE is stable, the stationary solution is used to obtain a solution which is almost periodic in distribution.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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