Bivariate Markov processes play a central role in the theory and applications of estimation, control, queuing, biomedical engineering, and reliability. Bivariate Markov Processes and Their Estimation presents some of the fundamentals of the theory of bivariate Markov processes, and reviews the various parameters and signal estimation approaches that are associated with these Markov processes. It reviews both causal and non-causal estimation of some statistics of the bivariate Markov processes. In addition, it covers off-line as well as on-line recursive parameter estimation approaches. Bivariate Markov Processes and Their Estimation is an ideal springboard for researchers and students who are interested in pursuing the study of this interesting family of processes. While proofs are generally omitted, an interested reader should be able to implement the estimation algorithms for bivariate Markov chains directly from the text. The material should be accessible to the signal processing community, although it requires some familiarity with Markov chains and the intricacies of the theory of hidden Markov models.