We study the h-transform of Doob for nonlocal branching processes, we show that the branching property is preserved provided that h is a coherent state, and we emphasize the probabilistic representation of the solution to the associated nonlinear evolution equation. The tools are from the analytic and probabilistic potential theory. We also investigate the h-transform of a subordinate \(C_0\)-semigroup of sub-Markovian operators on an \(L^p\) space.

中文翻译：

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Doob的h变换和非局部分支过程

我们研究了针对非局部分支过程的Doob的h变换，表明只要h是一个相干状态，分支性质就得以保留，并且我们着重指出了相关非线性演化方程解的概率表示。这些工具来自于分析和概率潜力理论。我们还调查了^ h下属的-transform \（C_0 \）上的子马氏运营商的-semigroup \（L ^ P \）空间。