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Journal Article

# Adaptive Simulation Using Perfect Control Variates

Shane G. Henderson and Burt Simon
Journal of Applied Probability
Vol. 41, No. 3 (Sep., 2004), pp. 859-876
Stable URL: http://www.jstor.org/stable/4141358
Page Count: 18

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## Abstract

We introduce adaptive-simulation schemes for estimating performance measures for stochastic systems based on the method of control variates. We consider several possible methods for adaptively tuning the control-variate estimators, and describe their asymptotic properties. Under certain assumptions, including the existence of a 'perfect control variate', all of the estimators considered converge faster than the canonical rate of n-1/2, where n is the simulation run length. Perfect control variates for a variety of stochastic processes can be constructed from 'approximating martingales'. We prove a central limit theorem for an adaptive estimator that converges at rate $n^{-1} \sqrt ln n$. A similar estimator converges at rate n-1. An exponential rate of convergence is also possible under suitable conditions.

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