A simple sequential stopping rule for Monte Carlo Simulation

In this paper, a sequential stopping rule for the estimation of a probability p by means of Monte Carlo simulation is analyzed. It is shown that the proposed estimator is almost unbiased, and guarantees a given relative precision irrespective of p. Under very mild conditions, the method also guarantees a certain confidence level for a given relative estimation error, provided that p does not exceed a maximum value. An extension to importance sampling is discussed.