The Laguerre process and generalized Hartman–Watson law
The Laguerre process and generalized Hartman–Watson law
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本文研究复Wishart过程或所谓的Laguerre过程$（X_t）_{t\geq0}$。我们感兴趣的特征值过程的行为，我们推导出一些有用的随机微分方程和计算的无穷小发电机和半群。我们还给出了不同指标之间的绝对连续关系。最后，我们计算了所谓的广义Hartman-沃森定律的密度函数，以及当矩阵的大小为2时，T_0：=\inf\{t，\det（X_t）=0\}的定律。
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.