Open Access
2006 On the Existence of Recurrent Extensions of Self-similar Markov Processes
Patrick Fitzsimmons
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Electron. Commun. Probab. 11: 230-241 (2006). DOI: 10.1214/ECP.v11-1222


Let $X= (X_t) _{t \geq 0}$ be a self-similar Markov process with values in the non-negative half-line, such that the state $0$ is a trap. We present a necessary and sufficient condition for the existence of a self-similar recurrent extension of $X$ that leaves $0$ continuously. This condition is expressed in terms of the Lévy process associated with $X$ by the Lamperti transformation.


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Patrick Fitzsimmons. "On the Existence of Recurrent Extensions of Self-similar Markov Processes." Electron. Commun. Probab. 11 230 - 241, 2006.


Accepted: 11 October 2006; Published: 2006
First available in Project Euclid: 4 June 2016

zbMATH: 1110.60036
MathSciNet: MR2266714
Digital Object Identifier: 10.1214/ECP.v11-1222

Primary: 60G18
Secondary: 60G51 , 60J45 , 60J55

Keywords: Cram'er condition , excursion , Lamperti transformation , recurrent extension , Self-similar , Semi-stable

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