## First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes ⋆

Citations: | 1 - 1 self |

### BibTeX

@MISC{Demni_firsthitting,

author = {Nizar Demni},

title = {First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes ⋆},

year = {}

}

### OpenURL

### Abstract

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. Key words: radial Dunkl processes; Weyl chambers; hitting time; multivariate special functions; generalized Hermite polynomials 2000 Mathematics Subject Classification: 33C20; 33C52; 60J60; 60J65 1

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Citation Context ...√t ∏ , y 〈α, y〉dy 1 They were called generalized Hermite polynomials in [20] but we prefer calling them as above to avoid the confusion with the generalized Hermite polynomials introduced by Lassalle =-=[17]-=-.First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes 3 where ∫ g(x) := C = ∏ α∈R+ 〈α, x √ t 〉 2l(α) e−|x|2 /2t e −|y|2 /2 D W k (x, y) ∏ Our key result is stated as follo... |