%0 Journal Article
%T First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
%A Nizar Demni
%J Mathematics
%D 2008
%I arXiv
%R 10.3842/SIGMA.2008.074
%X 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.
%U http://arxiv.org/abs/0811.0504v1