Stability of the exit time for Lévy processes
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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, τ u , it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τ u behaves linearly as u ↓ 0 or u → ∞. We also consider the conditional stability of τ u 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.
2011 ◽
Vol 43
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pp. 712-734
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2006 ◽
Vol 43
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pp. 967-983
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2006 ◽
Vol 43
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pp. 967-983
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2020 ◽
Vol 130
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pp. 1368-1387
2009 ◽
Vol 46
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pp. 542-558
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2016 ◽
Vol 53
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pp. 572-584
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1993 ◽
Vol 132
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pp. 141-153
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2006 ◽
Vol 38
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pp. 768-791
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2015 ◽
Vol 47
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pp. 128-145
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