First hitting time of the boundary of the Weyl chamber by radial Dunkl processes

Nizar Demni

doi:10.3842/SIGMA.2008.074

First hitting time of the boundary of the Weyl chamber by radial Dunkl processes

Nizar Demni

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	074
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	4
DOIs	https://doi.org/10.3842/SIGMA.2008.074
State	Published - 2008

Keywords

Generalized hermite polynomials
Hitting time
Multivariate special functions
Radial dunkl processes
Weyl chambers

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2008.074

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abstract = "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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AB - 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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KW - Multivariate special functions

KW - Radial dunkl processes

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ER -

First hitting time of the boundary of the Weyl chamber by radial Dunkl processes

Abstract

Keywords

ASJC Scopus subject areas

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