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 language | English (US) |
---|---|
Pages (from-to) | 556-580 |
Number of pages | 25 |
Journal | Bernoulli |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - 2007 |
Keywords
- Generalized Hartman-Watson law
- Gross-Richards formula
- Laguerre process
- Special functions of matrix argument
ASJC Scopus subject areas
- Statistics and Probability