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May 2007 The Laguerre process and generalized Hartman–Watson law
Nizar Demni
Bernoulli 13(2): 556-580 (May 2007). DOI: 10.3150/07-BEJ6048


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 $2$.


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Nizar Demni. "The Laguerre process and generalized Hartman–Watson law." Bernoulli 13 (2) 556 - 580, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1139.60037
MathSciNet: MR2331264
Digital Object Identifier: 10.3150/07-BEJ6048

Keywords: generalized Hartman–Watson law , Gross–Richards formula , Laguerre process , special functions of matrix argument

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 2 • May 2007
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