28 citations · 28 across the 4 of their papers we have counts for
6 papers · 1 filter
On a role of predictor in the filtering stability
P. Chigansky, R. Liptser
When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently availabl…
Stability of the nonlinear filter for slowly switching Markov chains
P. Chigansky
Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to inc…
An ergodic theorem for filtering with applications to stability
P. Chigansky
Ergodic properties of the signal-filtering pair are studied for continuous time finite Markov chains, observed in white noise. The obtained law of large numbers is applied to the s…
Stability of nonlinear filters in nonmixing case
Pavel Chigansky, Robert Liptser
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…
Asymptotic stability of the Wonham filter for ergodic and nonergodic signals
P. Baxendale, P. Chigansky, R. Liptser
Stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (…
On exponential stability of Wonham filter
P. Chigansky, R. Liptser
We give elementary proof of a stability result concerning an exponential asymptotic () for filtering estimates generated by wrongly initialized Wonham filter. This proo…