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Almost periodic solutions of affine Ito equations. (English) Zbl 0692.60045
Consider the affine Ito type stochastic differential equation $(1)\quad dx(t)=[A_ 0(t)x(t)+f_ 0(t)]dt+\sum^{m}_{j=1}[A_ j(t)x(t)+f_ j(t)]dw_ j(t),\quad t\in R,$ where $$A_ j:R\to R^ d\otimes R^ d$$, $$f_ j:R\to R^ d$$, $$0\leq j\leq m$$, are measurable and bounded. The authors discussed the problem of existence of almost periodic solutions of (1). It is proved that if the linear part of the affine equation is exponentially stable in mean square then the unique continuous $$L^ 2$$- bounded solution of the affine system has almost periodic one-dimensional distributions. An analogous result is shown for the asymptotic almost periodic case.
Reviewer: B.G.Pachpatte

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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