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Stability of the Exit Time for L'evy Processes | | Philip S. Griffin
; Ross A. Maller
; | | Date: |
27 Jun 2011 | | Abstract: | This paper is concerned with the behaviour of a L’{e}vy 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, $ au_u$, it takes the
process to transit above the level, and in particular, on the {it stability}
of this passage time; thus, essentially, whether or not $ au_u$ behaves
linearly as $udto 0$ or $u oinfty$. We also consider conditional stability
of $ au_u$ when the process drifts to $-infty$, a.s. This provides
information relevant to quantities associated with the ruin of an insurance
risk process, which we analyse under a Cram’er condition. | | Source: | arXiv, 1106.5389 | | Services: | Forum | Review | PDF | Favorites | |
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