Approximating martingales for variance reduction in Markov process simulation

‘Knowledge of either analytical or numerical approximations should enable more efficient simulation estimators to be constructed.’ This principle seems intuitively plausible and certainly attractive, yet no completely satisfactory general methodology has been developed to exploit it. The authors present a new approach for obtaining variance reduction in Markov process simulation that is applicable to a vast array of different performance measures. The approach relies on the construction of a martingale that is then used as an internal control variate.