TY - JOUR
T1 - Stability of nonlinear filters in nonmixing case
AU - Chigansky, Pavel
AU - Liptser, Robert
PY - 2004/11
Y1 - 2004/11
N2 - 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.
AB - 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.
KW - Filtering stability
KW - Geometric ergodicity
UR - http://www.scopus.com/inward/record.url?scp=26844508920&partnerID=8YFLogxK
U2 - 10.1214/105051604000000873
DO - 10.1214/105051604000000873
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AN - SCOPUS:26844508920
SN - 1050-5164
VL - 14
SP - 2038
EP - 2056
JO - Annals of Applied Probability
JF - Annals of Applied Probability
IS - 4
ER -