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Asymptotic almost periodic solutions for stochastic differential equations. (English) Zbl 0689.60060
Stochastic differential equations with asymptotic almost periodic coefficients are considered and sufficient conditions for a bounded solution to be asymptotically almost periodic in distribution are given. As in the case of deterministic equations a total stability concept is also necessary for stochastic differential equations but the trace of this concept in the deterministic case requires to use random vectors as initial conditions and to define equivalent stochastic differential equations since the weak convergence has to be replaced by a strong one in \(L_ 2\).
Reviewer: C.Vârsan

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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