On extrema of stable processes

Details On extrema of stable processes On extrema of stable processes

2010-01-07

arxiv.org/abs/1001.0991v3

Annals of Probability 2011, Vol. 39, No. 3, 1027-1060

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP577 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP577

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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