English

The Laguerre process and generalized Hartman--Watson law

Probability 2009-09-29 v1 Statistics Theory Statistics Theory

Abstract

In this paper, we study complex Wishart processes or the so-called Laguerre processes (Xt)t0(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 T0:=inf{t,det(Xt)=0}T_0:=\inf\{t,\det(X_t)=0\} when the size of the matrix is 2.

Cite

@article{arxiv.0708.4186,
  title  = {The Laguerre process and generalized Hartman--Watson law},
  author = {Nizar Demni},
  journal= {arXiv preprint arXiv:0708.4186},
  year   = {2009}
}

Comments

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)

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