This paper discusses likelihood ratio derivative estimation techniques for stochastic systems. After a brief review of the basic concepts, likelihood ratio derivative estimators are presented for the following classes of stochastic processes: time homogeneous discrete-time Markov chains, non-time homogeneous discrete-time Markov chains, time homogeneous continuous-time Markov chains, semi-Markov processes, non-time homogeneous continuous-time Markov chains, and generalized semi-Markov processes.
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Peter W. Glynn (1989) studied this question.