The Laguerre process and generalized Hartman--Watson law

Details The Laguerre process and generalized Hartman--Watson law The Laguerre process and generalized Hartman--Watson law

2007-08-30

arxiv.org/abs/0708.4186v1

Bernoulli 2007, Vol. 13, No. 2, 556-580

Mathematics

Probability

Published at http://dx.doi.org/10.3150/07-BEJ6048 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6048

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.

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