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Abstract: In this paper, we study complex Wishart processes or the so-called Laguerreprocesses $X t {t\geq0}$. We are interested in the behaviour of theeigenvalue process; we derive some useful stochastic differential equations andcompute both the infinitesimal generator and the semi-group. We also giveabsolute-continuity relations between different indices. Finally, we computethe density function of the so-called generalized Hartman-Watson law as wellas the law of $T 0:=\inf\{t,\detX t=0\}$ when the size of the matrix is 2.



Author: Nizar Demni

Source: https://arxiv.org/







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