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What is Learnable in Valiant's Theory of the Learnable? 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The Laguerre process and generalized Hartman--Watson law
Nizar Demni · 2007-08-30 · via math.ST updates on arXiv.org

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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