  In the last decade, there has been a growing interest to use Wishart
processes for modelling, especially for financial applications. However, there
are still few studies on the estimation of its parameters. Here, we study the
Maximum Likelihood Estimator (MLE) in order to estimate the drift parameters of
a Wishart process. We obtain precise convergence rates and limits for this
estimator in the ergodic case and in some nonergodic cases. We check that the
MLE achieves the optimal convergence rate in each case. Motivated by this
study, we also present new results on the Laplace transform that extend the
recent findings of Gnoatto and Grasselli and are of independent interest.
