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arXiv · 1001.0991

On extrema of stable processes

Alexey Kuznetsov
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Abstract

We study the Wiener--Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener--Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such as infinite series representations and asymptotic expansions for the density of supremum, explicit expressions for the Wiener--Hopf factors and the Mellin transform of the supremum, quasi-periodicity and functional identities for these functions, finite product representations in some special cases and identities in distribution satisfied by the supremum functional.

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Alexey Kuznetsov. 2010-01-07. On extrema of stable processes. https://doi.org/10.1214/10-aop577

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