2016 | OriginalPaper | Chapter
From Lévy to Feller Processes
Author : René Schilling
Published in: From Lévy-Type Processes to Parabolic SPDEs
Publisher: Springer International Publishing
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We have seen in Lemma 4.8 that the semigroup $$P_{t}f(x)\;:=\;\mathbb{E}^{x}f(X_{t})=\mathbb{E}f(X_{t}+x)$$ of a Lévy process $$(X_{t}){_t\geqslant0}$$ is a Feller semigroup.