Recurrent extensions of self-similar Markov processes and Cramér's condition
Let \(\xi\) be a real-valued Lévy process that satisfies Cramér's condition, and \(X\) a self-similar Markov process associated with \(\xi\) via Lamperti's transformation. The author proves the existence of a unique excursion measure \textbf{n}, compatible with the semigroup \(X\) and such that \({\mathbf n}(X_{0+}>0)=0\). Some descriptions of the measure \textbf{n} are given. Related paper: \textit{J. Lamperti} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 22, 205--225 (1972; Zbl 0274.60052)].
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