Laguerre Process and Generalised Hartman-Watson Law

摘要

In this paper, we study complex Wishart processes or the so-called Laguerreprocesses. 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, wecompute the density function of the generalised Hartman-Watson law as well asthe law of the first hitting time of 0 when the size m=2.