Stability of nonlinear filters in nonmixing case

• 成果类型: Article
• 署名作者: Chigansky, P; Liptser, R
• 署名单位: Tel Aviv University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000873
• 发表日期: 2004
• 页码: 2038-2056
• 关键词: Exponential stability

摘要

The nonlinear filtering equation is said to be stable if it forgets the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires stronger signal ergodicity provided by the, so called, mixing condition. The latter is formulated in terms of the transition probability density of the signal. The most restrictive requirement of the mixing condition is the uniform positiveness of this density. We show that it might be relaxed regardless of an observation process structure.