Abstract
We consider a random walk with a negative drift and with a jump distribution which under Cramr's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lvy process conditioned not to overshoot level 1. © 2010 Elsevier B.V. All rights reserved.
Original language | English |
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Pages (from-to) | 288-313 |
Number of pages | 26 |
Journal | Stochastic Processes and their Applications |
Volume | 121 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2011 |
Keywords
- borderline case
- convergence of conditional laws
- Random walk with negative drift
- spectrally positive lvy process conditioned not to overshoot
- tail asymptotics for the supremum