Laguerre Process and Generalised Hartman-Watson Law

Nizar Demni (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we study complex Wishart processes or the so-called Laguerre processes. We give some interest to the behaviour of the eigenvalues process, derive some useful SDE and compute both infinitesimal generator and semi-group. We also give absolute-continuity relations between different indices.Then, we compute the density function of the generalised Hartman-Watson law as well as the law of the first hitting time of 0 when the size m=2.

Mots clés: Laguerre process; generalised Hartman-Watson Law; Special functions of matrix argument; Gross-Richards formula

Domaines: Probabilités [math.PR]

Nizar Demni. Laguerre Process and Generalised Hartman-Watson Law. 2006. ⟨hal-00009439v3⟩