Moderate Deviations for Particle Filtering

Consider the state space model (Xt, Yt), where (Xt) is a Markov chain, and (Yt) are the observations. In order to solve the so-called 1 n n 1 δx i,t. In this paper we establish the moderate deviation principle for the empirical mean 1 n n 1 ψ(xi,t) (centered and properly rescaled) when the number of particles grows to infinity, enhancing the central limit theorem. Several extensions and examples are also studied.