Abstract
Conditions are given under which a semi-Markov process $Z(t)$ can be obtained from a Markov process $Y(t)$ by a time change (i.e. $Z(t) = Y(\gamma(t))$). Estimates are given for $P\{\sup_{s\leqq t} |s - \gamma(s)| > \varepsilon\}$ and the construction is used to give conditions under which a sequence of semi-Markov processes will have the same convergence properties as the corresponding sequence of Markov processes.
Citation
Thomas G. Kurtz. "Comparison of Semi-Markov and Markov Processes." Ann. Math. Statist. 42 (3) 991 - 1002, June, 1971. https://doi.org/10.1214/aoms/1177693327
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