Abstract
This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, u, starting from 0, both as u becomes large and as u becomes small. Our main focus is on the time, τu, it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τu behaves linearly as u ↓ 0 or u → ∞. We also consider the conditional stability of τu when the process drifts to -∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cramér condition.
Citation
Philip S. Griffin. Ross A. Maller. "Stability of the exit time for Lévy processes." Adv. in Appl. Probab. 43 (3) 712 - 734, September 2011. https://doi.org/10.1239/aap/1316792667
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