Geodesic
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients
Electronic journal of differential equations, Tome 2013 (2013)
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).
Classification : 34C27, 60H25, 34F05, 60H10
Keywords: square-mean almost periodic, almost periodic in distribution, Ornstein-Uhlenbeck, semilinear stochastic differential equation, stochastic evolution equation 
@article{EJDE_2013__2013__a125,
     author = {Mellah,  Omar and de Fitte,  Paul Raynaud},
     title = {Counterexamples to mean square almost periodicity of the solutions of some {SDEs} with almost periodic coefficients},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.60073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a125/}
}
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Mellah,  Omar; de Fitte,  Paul Raynaud. Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a125/