Recursive estimation of Hidden Markov Models

A recursive estimation method for Hidden Markov Models has been proposed in [24]. As suggested there the proposed recursive algorithm could be analyzed via the theory of stochastic approximations developed in [4]. The purpose of this note is to verify the basic probabilistic conditions of [4], given in Part II, Chapter 1 of [4]. For this purpose we consider a general class of Markov models in which a simple Markov process is passed through an exponentially stable non-linear system. The general theory is relatively easily applied to HMMs extended by their filter process and their derivatives, see [1].