A Particle Implementation

In this paper, the problem of identifying a hidden Markov model (HMM) with general state space, e.g. a partially observed diffusion process, is considered. A particle implementation of the recursive maximum likelihood estimator for a parameter in the transition kernel of the Markov chain is presented. The key assumption is that the derivative of the transition kernel w.r.t. the parameter has a probabilistic interpretation, suitable for Monte Carlo simulation. Examples are given to show that this assumption is satisfied in quite general situations. As a result, the linear tangent filter, i.e. the derivative of the filter w.r.t