Statistical Methods for Markov Processes

Abstract

In this chapter we deal with the estimation of Poisson processes, Markov chains, and Markov jump processes. It is shown that statistical estimation and tests concerning the transition matrix in Markov chains are asymptotically equivalent to those for one or more multinomial distributions. For this reason, and in order to provide an adequate link and streamline the notation, we also include some introductory sections revising the basic methods for multinomial distributions, which in turn will provide a rich methodology applicable to Markov chains and Markov processes (embedded chains).