Markov processes and linguistics

The Markov Matrix Model of languages, created to explain patterns observed in sequences of data, is briefly reviewed. It is then extended to multiple-stage Markov processes to include the history of the process, to Markov processes with higher connectivities, and to Markov processes with varying transition probabilities. It is found that the simple restricted model produces distributions with all the features of these extended models. Correlations in binary sequences produced by the Markov chain are reviewed and compared to correlations in a related, more restricted chain, which is open to analytical investigation. The analysis on this chain is presented, and conclusions are drawn which may also shed light on the more general case.