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

Omar Mellah (1, 2) , Paul Raynaud de Fitte (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées

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).

Mots clés: Square-mean almost periodic; almost periodic in distribution; Ornstein-Uhlenbeck; semilinear stochastic differential equation; stochastic evolution equation

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Omar Mellah, Paul Raynaud de Fitte. Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients. Electronic Journal of Differential Equations, 2013, 2013 (91), pp.1-7. ⟨hal-00726462⟩