First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes

We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W-inv...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2008
Main Author: Demni, N.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149001
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes / N. Demni // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 21 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Demni, N.
author_facet Demni, N.
citation_txt First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes / N. Demni // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 21 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W-invariant Dunkl-Hermite polynomials. Illustrative examples are given by the irreducible root systems of types A, B, D. The paper ends with an interest in the case of Brownian motions for which our formulae take determinantal forms.
first_indexed 2025-12-07T17:52:17Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T17:52:17Z
publishDate 2008
publisher Інститут математики НАН України
record_format dspace
spelling Demni, N.
2019-02-19T12:52:54Z
2019-02-19T12:52:54Z
2008
First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes / N. Demni // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 21 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 33C20; 33C52; 60J60; 60J65
https://nasplib.isofts.kiev.ua/handle/123456789/149001
We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W-invariant Dunkl-Hermite polynomials. Illustrative examples are given by the irreducible root systems of types A, B, D. The paper ends with an interest in the case of Brownian motions for which our formulae take determinantal forms.
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The author would like to thank C. Donati Martin for useful remarks and her careful reading of the paper, and P. Bougerol for explanations of some facts on root systems. He is grateful to M. Yor for his intensive reading of the manuscript and encouragements.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
Article
published earlier
spellingShingle First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
Demni, N.
title First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
title_full First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
title_fullStr First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
title_full_unstemmed First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
title_short First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
title_sort first hitting time of the boundary of the weyl chamber by radial dunkl processes
url https://nasplib.isofts.kiev.ua/handle/123456789/149001
work_keys_str_mv AT demnin firsthittingtimeoftheboundaryoftheweylchamberbyradialdunklprocesses