On the limit law of a random walk conditioned to reach a high level

We consider a random walk with a negative drift and with a jump distribution which under Cramér'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 Lévy process conditioned not to overshoot level 1.

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Year of publication:	2011
Authors:	Foss, Sergey G. ; Puhalskii, Anatolii A.
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 121.2011, 2, p. 288-313
Publisher:	Elsevier
Keywords:	Random walk with negative drift Tail asymptotics for the supremum Borderline case Convergence of conditional laws Spectrally positive Lévy process conditioned not to overshoot

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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