Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients

Abstract

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).

Cited by in corpus (3)

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• Periodic Solutions for SDEs through Upper and Lower Solutions
• Almost periodic solutions for stochastic differential equations with exponential dichotomy driven by Levy noise