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

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.

arXiv commentThis 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/

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Cited by in corpus (5)

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• Multiple-particle diffusion processes from the viewpoint of Dunkl operators: relaxation to the steady state
• First hitting time of the boundary of a wedge of angle $\pi /4$ by a radial Dunkl process
• Semilinear equations associated with Dunkl Laplacian