The Laguerre process and generalized Hartman-Watson law

Nizar Demni

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
Pages (from-to)556-580
Number of pages25
JournalBernoulli
Volume13
Issue number2
DOIs
StatePublished - 2007

Keywords

  • Generalized Hartman-Watson law
  • Gross-Richards formula
  • Laguerre process
  • Special functions of matrix argument

ASJC Scopus subject areas

  • Statistics and Probability

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