The Annals of Applied Probability

Stability of nonlinear filters in nonmixing case

Pavel Chigansky and Robert Liptser

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 4 (2004), 2038-2056.

Dates
First available in Project Euclid: 5 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1099674088

Digital Object Identifier
doi:10.1214/105051604000000873

Mathematical Reviews number (MathSciNet)
MR2099662

Zentralblatt MATH identifier
1065.93034

Subjects
Primary: 93E11: Filtering [See also 60G35] 60J57: Multiplicative functionals

Keywords
Filtering stability geometric ergodicity

Citation

Chigansky, Pavel; Liptser, Robert. Stability of nonlinear filters in nonmixing case. Ann. Appl. Probab. 14 (2004), no. 4, 2038--2056. doi:10.1214/105051604000000873. https://projecteuclid.org/euclid.aoap/1099674088


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