Stability of the optimal filter in a hidden Markov model with multiplicative noise

Abstract

We consider a hidden Markov model with multiplicative noise emerging from studies of software reliability. We show the stability of the optimal filter with respect to general initial conditions in the total variation- and $L^p$-norm and deduce explicit rates. Remarkably, stability turns out to be independent of the ergodic behavior of the signal.

11 pages

References in corpus (1)

• Uniform observability of hidden Markov models and filter stability for unstable signals