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

Tudor, Constantin

Stochastics Stochastics Rep. 38, No. 4, 251-266 (1992).

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.

Reviewer: H.Pragarauskas (Vilnius)

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

infinite-dimensional affine Itô equations; almost periodic coefficients