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 ...

We present here a new method to solve Markov chains based on a Stochastic Automata Network. This method merges the reduction technique and the nonsymmetric permutations on the rows and columns of the generator associated with the Markov chain. This method is developed to compute some rewards in a military application, but it happens that the method may have a larger field of interest.

In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M. Maxwell and M. Woodroofe [7] (2000). The main technique is the martingale argument and the theory of fractional coboundaries.

In this paper, a new technique for object classi cation from silhouettes is presented. Hidden Markov Models are used as a classi cation mechanism. Through a set of experiments, we show the validity of our approach and show its invariance under severe rotation conditions. Also, a comparison with other techniques that use Hidden Markov Models for object classi cation from silhouettes is presented.

In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M. Maxwell and M. Woodroofe [7] (2000). The main technique is the martingale argument and the theory of fractional coboundaries.

A 3D stochastic Navier-Stokes equation with a suitable non degenerate additive noise is considered. The regularity in the initial conditions of every Markov transition kernel associated to the equation is studied by a simple direct approach. A by-product of the technique is the equivalence of all transition probabilities associated to every Markov transition kernel.

We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results to Markov Chain Monte Carlo simulation. As another illustration, we use the method to derive a central limit theorem for U-statistics with varying kernels.

We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log-Det distance measure. We take as our...

We explore model-based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log-Det distance measure. We take as our...

Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996. Since then, several other such results have been proved; with few exceptions, these rely on coupling techniques. Though coupling is of unquestionable utility as a theoretical tool, it appears to have some limitations. Coupling has yet to ...