Ergodicity of hidden Markov models

被引：13
|
作者：
Di Masi, GB
Stettner, L
机构：
[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
[2] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35131 Padua, Italy
[3] CNR, ISIB, I-35131 Padua, Italy
来源：
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2005年 / 17卷 / 04期
关键词：
nonlinear filtering process; invariant measures; asymptotic stability;
D O I：
10.1007/s00498-005-0153-8
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper we study ergodic properties of hidden Markov models with a generalized observation structure. In particular sufficient conditions for the existence of a unique invariant measure for the pair filter-observation are given. Furthermore, necessary and sufficient conditions for the existence of a unique invariant measure of the triple state-observation-filter are provided in terms of asymptotic stability in probability of incorrectly initialized filters. We also study the asymptotic properties of the filter and of the state estimator based on the observations as well as on the knowledge of the initial state. Their connection with minimal and maximal invariant measures is also studied.
引用
收藏
页码：269 / 296
页数：28
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