Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes
type: Item
instance of: scholarly article
title: Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes
zbMATH Open document ID: 1268.60060
published in: Acta Applicandae Mathematicae
publication date: 2013-02-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1012.0817
review text: The authors study exponential functionals of hypergeometric Lévy processes which include, for instance, the Lamperi-stable processes. The Mellin transform as well as convergent and asymptotic series representations are obtained for the density of the exponential functional. The proof relies on a verification result which gives explicit conditions to identify the Mellin transform uniquely. The results are applied to fluctuations of stable processes. In particular, they determine densities of the supremum of stable processes, of the entrance law of the excursion measure of a stable processes reflected at its past infimum, and of the entrance law of a stable process conditioned to stay positive. Further results on multidimensional symmetric stable processes are obtained.
reviewed by: Mathias Trabs
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G52
zbMATH DE Number: 6133842
zbMATH Keywords: hypergeometric Lévy processes
zbMATH Keywords: Lamperti-stable processes
zbMATH Keywords: exponential functional
zbMATH Keywords: Mellin and Lamperti transform
zbMATH Keywords: convergent and asymptotic series expansion
zbMATH Keywords: extrema of stable processes
author: Alexey Kuznetsov
author: J. C. Pardo
MaRDI profile type: Publication
OpenAlex ID: W2122487927
arXiv ID: 1012.0817
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DOI: 10.1007/S10440-012-9718-Y
description: scientific article