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On the Existence of Recurrent Extensions of Self-similar Markov Processes

   
@article{ECP1222,
	author = {Patrick Fitzsimmons},
	title = {On the Existence of Recurrent Extensions of Self-similar Markov Processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {11},
	year = {2006},
	keywords = {self-similar, semi-stable, Lamperti transformation, recurrent extension, Cram'er condition, excursion},
	abstract = {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.},
	pages = {no. 25, 230-241},
	issn = {1083-589X},
	doi = {10.1214/ECP.v11-1222},    
        url = {http://ecp.ejpecp.org/article/view/1222}}