Geodesic
First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: radial Dunkl processes; Weyl chambers; hitting time; multivariate special functions; generalized Hermite polynomials. 
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     author = {Nizar Demni},
     title = {First {Hitting} {Time} of the {Boundary} of the {Weyl} {Chamber} by {Radial} {Dunkl} {Processes}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a73/}
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Nizar Demni. First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a73/

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