A novel approach to the global attracting sets of mild solutions for stochastic functional partial differential equations driven by Lévy noise is presented. Consequently, some new sufficient conditions ensuring the existence of the global attracting sets of mild solutions for the considered equations are established. As applications, some new criteria for the exponential stability in mean square of the considered equations is obtained. Subsequently, by employing a weak convergence approach, we try to establish some stability conditions in distribution of the segment processes of mild solutions to stochastic delay partial differential equations with jumps under some weak conditions. Some known results are improved. Lastly, some examples are investigated to illustrate the theory.

提出了一种新颖的方法，用于求解由Lévy噪声驱动的随机泛函偏微分方程的温和解的全局吸引集。因此，建立了一些新的充分条件，以确保所考虑方程的全局吸引性温和解集的存在。作为应用，获得了考虑方程的均方指数稳定性的一些新准则。随后，通过采用弱收敛方法，我们尝试建立了在某些弱条件下具有时滞的随机时滞偏微分方程的温和解分段过程的分布的稳定性条件。一些已知的结果得到了改善。最后，研究了一些例子来说明这一理论。