On Error-free Filtering of Finite-State Singular Processes under Dependent Distortions

We consider 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, the causal error-free (with probability one) filtering is possible.