%0 Journal Article
%T The Laguerre process and generalized Hartman--Watson law
%A Nizar Demni
%J Mathematics
%D 2007
%I arXiv
%R 10.3150/07-BEJ6048
%X In this paper, we study complex Wishart processes or the so-called Laguerre processes $(X_t)_{t\geq0}$. We are interested in the behaviour of the eigenvalue process; we derive some useful stochastic differential equations and compute both the infinitesimal generator and the semi-group. We also give absolute-continuity relations between different indices. Finally, we compute the density function of the so-called generalized Hartman--Watson law as well as the law of $T_0:=\inf\{t,\det(X_t)=0\}$ when the size of the matrix is 2.
%U http://arxiv.org/abs/0708.4186v1