The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 14, Number 4 (2004), 2038-2056.
Stability of nonlinear filters in nonmixing case
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.
Ann. Appl. Probab., Volume 14, Number 4 (2004), 2038-2056.
First available in Project Euclid: 5 November 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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