Variance of Statistical Parameter Estimates of a Semimarkov Process with a Finite State Space

We consider statistical estimates of parameter of a generalized semi-Markov process with a finite state space. The estimates take the form of a ratio of two accumulative processes in time $t$. It is shown that the estimates are asymptotically unbiased, consistent, and asymptotically normal as $t\to\infty$. Formulas for the variance of the estimates are obtained.