3 papers
math.PR2005
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…
math.PR2004
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…
math.PR2004
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…