Laguerre Process and Generalised Hartman-Watson Law

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.