The Laguerre process and generalized Hartman--Watson law

Abstract

In this paper, we study complex Wishart processes or the so-called Laguerre processes $(X_t{)}_{t\ge 0}$. 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.

Published at http://dx.doi.org/10.3150/07-BEJ6048 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems

Cited by in corpus (1)

• Radial Dunkl Processes : Existence and uniqueness, Hitting time, Beta Processes and Random Matrices