In this paper, we introduce the concepts of $𝜃$-remotely almost periodic processes and remotely almost periodicity in distribution. Under the framework of evolution system, we establish $𝜃$-remotely almost periodicity and remotely almost periodicity in distribution for solutions to stochastic differential equations (SDEs) $$dX(t)=A(t)X(t)dt+F(t,X(t))dt+G(t,X(t))dW(t),t\in ℝ$$ in infinite dimensions. Our main results extend some earlier results about the above SDEs in the cases of $A(t)\equiv A$ and almost periodic coefficients, without assuming that $A(t)$ is periodic as in a classical result by Da Prato and Tudor. The main difficulties lie in the loss of compactness for $𝜃$-remotely almost periodic processes and the delicate analysis caused by evolution system. Moreover, our abstract results can be applied to some stochastic parabolic partial differential equations.

在本文中，我们介绍了以下概念$𝜃$-远程几乎周期性过程和远程几乎周期性分布。在进化系统的框架下，我们建立$𝜃$- 随机微分方程 (SDE) 解的分布中的远程几乎周期性和远程几乎周期性$$dX（t）=A（t）X（t）dt+F（t,X（t））dt+G（t,X（t））d瓦（t）,t\epsilon ℝ$$在无限维度中。我们的主要结果扩展了关于上述 SDE 的一些早期结果：$A（t）==A$和几乎周期性系数，而不假设$A（t）$是周期性的，正如 Da Prato 和 Tudor 的经典结果一样。主要困难在于失去紧凑性$𝜃$-远近周期过程和演化系统引起的精细分析。此外，我们的抽象结果可以应用于一些随机抛物型偏微分方程。