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Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients. (English) Zbl 1288.60073
Summary: We show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost periodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution).

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
60H25 Random operators and equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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