Particle filters for partially observed Markov Chains

We consider particle filters in a model where the hidden states and the observations form jointly a Markov Chain, which means that the hidden states alone do not necessarily form a Markov chain. This model includes as a special case non-linear state-space models with correlated Gaussian noise. Our contribution is to study propagation of errors, stability properties of the filter, and uniform error estimates, using the framework of LeGland and Oudjane.