This paper provides a general and abstract approach to compute invariant distributions for Feller processes. More precisely, we show that the recursive algorithm presented in [10] and based on simulation algorithms of stochastic schemes with decreasing steps can be used to build invariant measures for general Feller processes. We also propose various applications: Approximation of Markov Brownian diffusion stationary regimes with Milstein or Euler scheme and approximation of Markov switching Brownian diffusion stationary regimes using Euler scheme.In this section, we show that the empirical measures defined in the same way as in (1) and built from an approximation (X γ Γn ) n∈N of a Feller process (X t ) t 0 (which are not specified explicitly), where the step sequence (γ n ) n∈N * → n→+∞ 0, a.s. weakly converges the set V, of the invariant distributions of (X t ) t 0 . To this end, we will provide as weak as possible mean reverting assumptions on the pseudo-generator of (X γ Γn ) n∈N on the one hand and appropriate rate conditions on the step sequence (γ n ) n∈N * on the other hand. Presentation of the abstract framework NotationsLet (E, |.|) be a locally compact separable metric space, we denote C(E) the set of continuous functions on E and C 0 (E) the set of continuous functions that vanish a infinity. We equip this space with the sup norm f ∞ = sup x∈E |f (x)| so that (C 0 (E), . ∞ ) is a Banach space. We will denote

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 [17] and are of independent interest.

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