  This paper provides a general and abstract approach to approximate ergodic
regimes of Markov and Feller processes. More precisely, we show that the
recursive algorithm presented in Lamberton & Pages (2002) and based on
simulation algorithms of stochastic schemes with decreasing step can be used to
build invariant measures for general Markov and Feller processes. We also
propose applications in three different configurations: Approximation of Markov
switching Brownian diffusion ergodic regimes using Euler scheme, approximation
of Markov Brownian diffusion ergodic regimes with Milstein scheme and
approximation of general diffusions with jump components ergodic regimes.
