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 $g$.

中文翻译：

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随机微分方程的周期、准周期、近周期、近自守、Birkhoff 循环和泊松稳定解

论文致力于研究泊松稳定性问题（特别是平稳性、周期性、准周期性、玻尔近似周期性、玻尔近似自同构、伯克霍夫递归、Bebutov意义上的近似递归、列维坦近似周期性、伪周期、伪-递归，泊松稳定性）半线性随机方程的解 $$ dx(t)=(Ax(t)+f(t,x(t)))dt +g(t,x(t))dW( t)\quad (*) $$ 具有指数稳定的线性算子 $A$ 和泊松稳定的时间系数 $f$ 和 $g$。我们证明，如果函数 $f$ 和 $g$ 适当地“小”，则方程 $(*)$ 承认至少一个与函数 $f$ 和 $g$ 具有相同递归特征的解。