The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) isa powerful alternative to EM when the E-step is intractable. Convergence ofSAEM toward a maximum of the observed likelihood is established whenthe unobserved data are simulated at each iteration under the conditionaldistribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximationwith Markovian perturbations are used to establish the convergenceof SAEM when it is coupled with a Markov chain Monte-Carloprocedure. This result is very useful for many practical applications. Applications to the convolution model and the change-points model are presented to illustrate the proposed method.
