Stability properties of some particle filters

Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the non-asymptotic, relative variance associated with the particle approximation of the normalizing constant is bounded linearly in time. The conditions are demonstrated to hold for some hidden Markov models on non-compact state spaces. The particle stability results are obtained by proving v-norm multiplicative stability and exponential moment results for the underlying Feynman-Kac formulae.