We study properties and parameter estimation of finite-state homogeneous continuous-time bivariate Markov chains. Only one of the two processes of the bivariate Markov chain is observable. The general form of the bivariate Markov chain studied here makes no assumptions on the structure of the generator of the chain, and hence, neither the underlying process nor the observable process is necessa...

The paper presents a quick and simpli ed aggregation method for a large class of Markov chain functionals based on the concept of stochastic complementation. Aggregation results in a reduction in the number of Markov states by grouping them into a smaller number of aggregated states, thereby producing a considerable saving on computational complexity associated with maximum likelihood parameter...

.................................................................................................................... 2 Preface ....................................................................................................................... 3 Acknowledgements................................................................................................... 4 Chapter 1: Introduction .........

This paper presents a complete framework for the testing procedure based on statistical theory of Markov chains. First, based on this methodology, an analytical evaluation of the Markov representation of time series is undertaken. It is shown that there is a one-to-one correspondence between the AR(1) parameter and the transition probability matrix of the Markov representation of that series. U...

We give an account of some results, both old and new, about any n× n Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.