Optimum Biasing of Integral Equations in Monte Carlo Calculations

In solving integral equations and estimating average with the Monte Carlo method, biasing functions may be used to reduce the variance of the estimates. A simple derivation has been used to prove the existence of a zero-variance collision estimator if a specific biasing function and survival probability are applied. This optimum biasing function is the same as that used for the well-known zero-variance last-event estimator.