On convergence of recursive Monte Carlo filters in non-compact state spaces

Abstract

We consider the particle lter approximation of the optimal lter in non-compact state space models. A time-uniform convergence result is built on top of a lter stability argument developed by Douc, Moulines, and Ritov (2009), under the assumption of a heavy-tailed state process and an informative observation model. We show that an existing set of sucient conditions for lter stability is also sucient, with minor modications, for particle lter convergence. The rate of convergence is also given and depends on both the sample size and the tail behavior of the transition kernel.