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Almost periodic solutions of affine stochastic evolution equations. (English) Zbl 0752.60049

The infinite-dimensional affine Itô equations with almost periodic coefficients are studied. It is proved that one-dimensional distributions of the solution are almost periodic if they are relatively compact and the solution of the linear part of the equation is \(L^ 2\)-exponentially stable. A similar result is obtained for equations with asymptotically almost periodic coefficients.

MSC:

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