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First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
Інший ID:
2000 Mathematics Subject Classification: 33C20; 33C52; 60J60; 60J65
Посилання:
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.
Підтримка:
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.
Дата:
2008
Переглядів:
474
Завантажень:
203
Анотація:
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.
