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arXiv · 0712.2637

On the Limit Law of a Random Walk Conditioned to Reach a High Level

Sergey G. Foss·Anatolii A. Puhalskii
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Abstract

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 %-Khinchin process conditioned not to overshoot level one.

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Sergey G. Foss, Anatolii A. Puhalskii. 2012-08-17. On the Limit Law of a Random Walk Conditioned to Reach a High Level. https://arxiv.org/abs/0712.2637

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