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Functional Limit Theorems for Lévy Processes Satisfying Cramér's Condition

   
@article{EJP930,
	author = {Matyas Barczy and Jean Bertoin},
	title = {Functional Limit Theorems for Lévy Processes Satisfying Cramér's Condition},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {Lévy process; Cramér's condition; self-similar Markov process},
	abstract = {We consider a Lévy process that starts from $x<0$ and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as $x$ goes to $-\infty$ for the law of the (two-sided) path shifted at the first instant when it enters $(0,\infty)$, respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.},
	pages = {no. 73, 2020-2038},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-930},    
        url = {http://ejp.ejpecp.org/article/view/930}}