Unimodality of hitting times for stable processes

Julien Letemplier; Thomas Simon

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arXiv · 1309.5321

Unimodality of hitting times for stable processes

Julien Letemplier·Thomas Simon

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Abstract

We show that the hitting times for points of real $α-$stable Lévy processes ($1<α\le 2$) are unimodal random variables. The argument relies on strong unimodality and several recent multiplicative identities in law. In the symmetric case we use a factorization of Yano et al., whereas in the completely asymmetric case we apply an identity of the second author. The method extends to the general case thanks to a fractional moment evaluation due to Kuznetsov et al.

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Julien Letemplier, Thomas Simon. 2013-11-07. Unimodality of hitting times for stable processes. https://arxiv.org/abs/1309.5321

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