Derivative Estimates From Discontinuous Realizations: Smoothing Techniques.

We develop two methods for estimating derivatives of expectations from simulation of functions whose realizations are discontinuous in the parameter of differentiation. We take as motivating example the estimation of the sensitivity of expected terminal reward for processes on discrete state spaces. Both our methods use conditional expectations to smooth discontinuities. The first smooths the dependence on the differentiation parameter, while the second smooths dependence on the time parameter. The methods are illustrated through examples, including stochastic networks, networks of queues, and Markov processes. Some of our results are obtained by specializing earlier work on generalized semi-Markov processes.