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Recurrent extensions of self-similar Markov processes and Cramér’s condition. II. (English) Zbl 1132.60056
Summary: We prove that a positive self-similar Markov process $$(X, \mathbb P)$$ that hits 0 in a finite time admits a self-similar recurrent extension that leaves 0 continuously if and only if the underlying Lévy process satisfies Cramér’s condition.
For part I, see ibid. 11, No. 3, 471–509 (2005; Zbl 1077.60055).

##### MSC:
 60J25 Continuous-time Markov processes on general state spaces 60G18 Self-similar stochastic processes
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