2009/10/31 by Pavel Chigansky, Ramon van Handel · 16 citations
Computer Science · Engineering · Mathematics · #Countable set #Ergodic theory #Ergodicity #Markov Chains and Monte Carlo Methods #Markov chain #Markov process #Mathematical proof #Measure (data warehouse) #Stability and Control of Uncertain Systems #Target Tracking and Data Fusion in Sensor Networks #Uniqueness #Variable-order Markov model #cs.IT #math.IT #math.PR
paper · pdf · doi:10.1214/10-aap688
published in The Annals of Applied Probability 20(6) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/10-AAP688 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2010/10/19 · arxiv created 2010/11/15 · arxiv updated 2010/11/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We develop necessary and sufficient conditions for uniqueness of the invariant measure of the filtering process associated to an ergodic hidden Markov model in a finite or countable state space. These results provide a complete solution to a problem posed by Blackwell (1957), and subsume earlier partial results due to Kaijser, Kochman and Reeds. The proofs of our main results are based on the stability theory of nonlinear filters.