Abstract
In this paper, we study complex Wishart processes or the so-called Laguerre processes $(X_t)_{t≥0}$. 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 $2$.
Citation
Nizar Demni. "The Laguerre process and generalized Hartman–Watson law." Bernoulli 13 (2) 556 - 580, May 2007. https://doi.org/10.3150/07-BEJ6048
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