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

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

2008-11-04

arxiv.org/abs/0811.0504v1

SIGMA 4 (2008), 074, 14 pages

Mathematics

Probability

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability

Scientific paper

10.3842/SIGMA.2008.074

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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