We prove limit theorems for cylindrical martingale problems associated with Lévy generators. Furthermore, we give sufficient and necessary conditions for the Feller property of well-posed problems with continuous coefficients. We discuss two applications. First, we derive continuity and linear growth conditions for the existence of weak solutions to infinite-dimensional stochastic differential equations driven by Lévy noise. Second, we derive continuity, local boundedness and linear growth conditions for limit theorems and the Feller property of weak solutions to stochastic partial differential equations driven by Wiener noise.

中文翻译：

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与 Lévy 发生器相关的圆柱鞅问题的极限定理

我们证明了与 Lévy 生成器相关的圆柱鞅问题的极限定理。此外，我们给出了连续系数适定问题的 Feller 性质的充分必要条件。我们讨论两个应用程序。首先，我们推导出由 Lévy 噪声驱动的无限维随机微分方程弱解存在的连续性和线性增长条件。其次，我们推导了极限定理的连续性、局部有界性和线性增长条件以及由维纳噪声驱动的随机偏微分方程弱解的 Feller 性质。