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The paper is dedicated to studying the problem of Poisson stability (inparticular stationarity, periodicity, quasi-periodicity, Bohr almostperiodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence inthe sense of Bebutov, Levitan almost periodicity, pseudo-periodicity,pseudo-recurrence, Poisson stability) of solutions for semi-linear stochasticequation $$ dx(t)=(Ax(t)+f(t,x(t)))dt +g(t,x(t))dW(t)\quad (*) $$ withexponentially stable linear operator $A$ and Poisson stable in timecoefficients $f$ and $g$. We prove that if the functions $f$ and $g$ areappropriately "small", then equation $(*)$ admits at least one solution whichhas the same character of recurrence as the functions $f$ and $g$.

Periodic, Quasi-Periodic, Almost Periodic, Almost Automorphic, Birkhoff Recurrent and Poisson Stable Solutions for Stochastic Differential Equations