A local limit theorem for hidden Markov chains

Central and Local Limit Theories in Markov Dependent Random Variables

Taylor Expansion for the Entropy Rate of Hidden Markov Chains

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 ...

Isometric Cocycles Related to Beam Splittings

We provide in the context of quantum Markov chains due to Accardi coming up from iterated beam splittings a limit theorem concerning with a refinement of the discrete time. The limit object refers to a continuous time and should be called quantum Markov process. Closely related to our construction of such quantum Markov processes are isometric cocycles. We derive, upto technical conditions, a c...

A Local Limit Theorem for a Family of Non-reversible Markov Chains

Abstract. By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identical smaller chains around a directed cycle, are not reversible, have little symmetry, do not have uniform stationary distributions, and can be nearly periodic, prior general bounds on rates of c...

Relative Entropy Rate between a Markov Chain and Its Corresponding Hidden Markov Chain

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...