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.Comment: This is a contribution to the Special Issue on Dunkl Operators and
Related Topics, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
