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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149001 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862714600081850368 |
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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.
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| first_indexed | 2025-12-07T17:52:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149001 |
| 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 |