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arXiv · 0708.4186

The Laguerre process and generalized Hartman--Watson law

Nizar Demni
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Abstract

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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Nizar Demni. 2007-08-30. The Laguerre process and generalized Hartman--Watson law. https://doi.org/10.3150/07-bej6048

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