  The paper is dedicated to studying the problem of Poisson stability (in
particular stationarity, periodicity, quasi-periodicity, Bohr almost
periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in
the sense of Bebutov, Levitan almost periodicity, pseudo-periodicity,
pseudo-recurrence, Poisson stability) of solutions for semi-linear stochastic
equation $$ dx(t)=(Ax(t)+f(t,x(t)))dt +g(t,x(t))dW(t)\quad (*) $$ with
exponentially stable linear operator $A$ and Poisson stable in time
coefficients $f$ and $g$. We prove that if the functions $f$ and $g$ are
appropriately "small", then equation $(*)$ admits at least one solution which
has the same character of recurrence as the functions $f$ and $g$.
