A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains

Autor:	Chigansky, Pavel, van Handel, Ramon
Rok vydání:	2009
Předmět:	Mathematics - Probability Computer Science - Information Theory
Zdroj:	Annals of Applied Probability 2010, Vol. 20, No. 6, 2318-2345
Druh dokumentu:	Working Paper
DOI:	10.1214/10-AAP688
Popis:	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. Comment: 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)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0910.3603 Zobrazit plný text záznamu View this record from Arxiv