Using martingales to make stochastic simulations more precise

This paper proposes a new form of control statistics to improve the efficiency of stochastic simulations. They are martingales composed of the sum of a number of increments whose expectation given previous increments is zero, and are a potentially powerful generalisation of the control statistics currently in use. The approach is illustrated on a simple example where its effectiveness in estimating both the mean and variance of a response variable is shown.