In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-periodic, pseudo-recurrent and Poisson stable) solutions for semilinear stochastic differential equations driven by infinite dimensional Lévy noise with large jumps. Under suitable conditions on drift, diffusion and jump coefficients, we prove that there exist solutions which inherit the Poisson stability of coefficients. Further we show that these solutions are globally asymptotically stable in square-mean sense. Finally, we illustrate our theoretical results by several examples.

在本文中，我们使用统一的框架来研究Poisson稳定性（包括平稳，周期性，准周期性，几乎周期性，几乎自同构，Birkhoff递归，Bebutov意义上的几乎递归，Levitan几乎周期性，伪周期，伪随机性）。无限维Lévy噪声驱动的具有大跳变的半线性随机微分方程的递归和Poisson稳定）解。在适当的漂移，扩散和跳跃系数条件下，我们证明了存在继承系数的泊松稳定性的解。进一步，我们证明这些解在平方均值意义上是全局渐近稳定的。最后，我们通过几个例子说明我们的理论结果。