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Passage time and fluctuation calculations for subexponential Lévy processes

Doney, Ron; Klüppelberg, Claudia; Maller, Ross


We consider the passage time problem for Lévy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to −∞ a.s. of the process, possibly at a linear rate (the finite mean case), but possibly much faster (the infinite mean case), together with subexponential growth on the positive side. Local and functional versions of limit distributions are derived for the passage time itself, as well as for the position of the process just prior to...[Show more]

CollectionsANU Research Publications
Date published: 2016
Type: Journal article
Source: Bernoulli
DOI: 10.3150/15-BEJ700
Access Rights: Open Access


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