Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 91, pp. 1-7.
Title: Counterexamples to mean square almost periodicity of
the solutions of some SDEs with almost periodic coefficients
Authors: Omar Mellah (Univ. of Tizi-Ouzou, Algeria)
Paul Raynaud de Fitte (Normandie Univ., Rouen, France)
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).
Submitted September 18, 2012. Published April 05, 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.