Electron. J. Diff. Equ., Vol. 2013 (2013), No. 91, pp. 1-7.

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

Omar Mellah, Paul Raynaud de Fitte

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).

Submitted September 18, 2012. Published April 5, 2013.
Math Subject Classifications: 34C27, 60H25, 34F05, 60H10.
Key Words: Square-mean almost periodic; almost periodic in distribution; Ornstein-Uhlenbeck; semilinear stochastic differential equation; stochastic evolution equation.

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Omar Mellah
Department of Mathematics Faculty of Sciences
University of Tizi-Ouzou, Algeria.
Normandie Univ, Lab. Rapha\"el Salem
UMR CNRS 6085, Rouen, France
email: omellah@yahoo.fr
Paul Raynaud de Fitte
Normandie Univ., Laboratoire Rapha\"el Salem
UMR CNRS 6085, Rouen, France
email: prf@univ-rouen.fr

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