A BIVARIATE COUNTING PROCESS

We consider a bivariate Markov counting process with transition probab ilities having a particular structure, which includes a number of usef ul population processes. Using a suitable random time-scale transforma tion, we derive some probability statements about the process and some asymptotic results. These asymptotic results are also derived using m artingale methods. Further, it is shown that these methods and results can be used for inference on the rate parameters for the process. The general epidemic model and the square law conflict model are used as illustrative examples.