On extrema of stable processes
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.
Cite
@article{arxiv.1001.0991,
title = {On extrema of stable processes},
author = {Alexey Kuznetsov},
journal= {arXiv preprint arXiv:1001.0991},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP577 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)