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This article is cited in 9 scientific papers (total in 9 papers)
First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
Nizar Demni SFB 701, Fakultät für Mathematik, Universität Bielefeld, Deutschland
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.
Keywords:
radial Dunkl processes; Weyl chambers; hitting time; multivariate special functions; generalized Hermite polynomials.
Received: July 1, 2008; in final form October 24, 2008; Published online November 4, 2008
Citation:
Nizar Demni, “First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes”, SIGMA, 4 (2008), 074, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma327 https://www.mathnet.ru/eng/sigma/v4/p74
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Abstract page: | 203 | Full-text PDF : | 37 | References: | 27 |
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