Asymptotic almost periodic solutions for stochastic differential equations. (English) Zbl 0689.60060

Vârsan, Constantin

Tôhoku Math. J., II. Ser. 41, No. 4, 609-618 (1989).

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)

Keywords:

asymptotic almost periodic solutions; Stochastic differential equations; almost periodic coefficients; weak convergence

References:

[1]	T. YOSHIZAWA, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer-Verlag, Applied Mathematical Sciences 14, 1975 · Zbl 0304.34051
[2]	Y. HINO AND T. YOSHIZAWA, Total Stability Property in Limiting Equations for a Functional Differentia Eauation with Infinite Delay, Casopis pre pestovani matematiky, roc 111 (1986) Praha. · Zbl 0599.34071 · eudml:21631
[3]	C CORDUNEANU, Almost Periodic Functions, Interscience Publishers, Interscience Tracts in Pure an Applied Mathematics, Nr 22, 1968 · Zbl 0175.09101
[4]	N. IKEDA AND S WATANABE, Stochastic Differential Equations and Diffusion Processes, North Holland, 1981 · Zbl 0495.60005