We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to nondensely defined operators. We show how it can be applied to piecewise deterministic Markov processes and transport equations with abstract boundary conditions. We give particular examples to illustrate our results.

中文翻译：

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边界条件的输运方程和扰动

我们为抽象AL空间上的亚随机半群提供了新的摄动定理，将Kato的摄动定理扩展到非密集定义的算子。我们展示了如何将其应用于具有抽象边界条件的分段确定性马尔可夫过程和运输方程。我们举一些具体的例子来说明我们的结果。