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.
- borderline case
- convergence of conditional laws
- Random walk with negative drift
- spectrally positive lvy process conditioned not to overshoot
- tail asymptotics for the supremum