The present paper is concerned with the estimation of the transition distributions of a Markov renewal process with finitely many states, which extends and unifies some aspects of the results in the special cases of discrete and continuous parameter Markov chains. A natural estimator of the transition distributions is defined and shown to be consistent. Limiting distributions of this estimator are derived. A density for a Markov renewal process is developed to permit the definition of maximum likelihood estimators for a renewal process and for a Markov renewal process.
Prepared in cooperation with Washington Univ., Seattle. DOI: 10.21236/AD0607350