Abstract The generalized perturbative approach is an all-purpose variant of Stein’s method used to obtain rates normal approximation. Originally developed for functions independent random variables, this here extended the realization a hidden Markov model. In dependent setting, convergence are provided in some applications, leading, each instance, extra log-factor vis-à-vis rate case.

It reviews the theory of Hidden Filter Hidden Markov Models and presents an extension, Mixed State Hidden Markov Models, developed jointly by Andrew Fraser and myself under his supervision. This manuscript version has only trivial differences from the original.

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing the probability of generating a given string, or computing the most likely path generating a given...