On the error-free filtering of finite-state singular processes under dependent distortions (Q941876)

This paper considers the problem of finding some sufficient conditions under which causal error-free filtering for a singular stationary stochastic process \(X =\{X_n\}\) with a finite number of states from noisy observations is possible. For a rather general model of observations, where the observable stationary process is absolutely regular with respect to the estimated process \(X\), it is proved (using an information-theoretic approach) that under a natural additional condition, causal error-free (with probability one) filtering is possible. For the authors' letter to the editors concerning the validity of the main theorem see [Probl. Inf. Transm. 45, No. 2, 191 (2009); translation from Probl. Peredachi Inf. 45, No. 2, 127 (2009; Zbl 1334.62148)].