We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space. This is applied to develop a theory of SPDEs with rather general coefficients. In particular, we can then study SPDEs driven by general Lévy processes in this context.

中文翻译：

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由核空间对偶跃迁驱动的随机积分和随机PDE

我们开发了一种新的弱和强随机积分理论，用于对cylindrical值在核空间对偶中的圆柱cylindrical值测量。这被用来发展具有相当一般系数的SPDE的理论。特别是，我们可以在这种情况下研究由一般Lévy流程驱动的SPDE。