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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| Date: | 2008 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149001 |
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| 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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irk-123456789-1490012019-02-20T01:24:12Z First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes Demni, N. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149001 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Demni, N. |
| spellingShingle |
Demni, N. First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Demni, N. |
| author_sort |
Demni, N. |
| title |
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_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_sort |
first hitting time of the boundary of the weyl chamber by radial dunkl processes |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149001 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT demnin firsthittingtimeoftheboundaryoftheweylchamberbyradialdunklprocesses |
| first_indexed |
2023-05-20T17:31:36Z |
| last_indexed |
2023-05-20T17:31:36Z |
| _version_ |
1796153498917666816 |