Monte Carlo Variance Comparison for Expected-Value Versus Sampled Splitting

Splitting techniques are among the most common and successful variance reduction techniques used in Monte Carlo calculations. The simplest type of splitting occurs when the splitting ratio, v, is an integer. In this case, one particle of weight w is replaced by v particles of weight wv⁻¹. Often, v is specified as a ratio of two numbers. In these cases, v need not be an integer. Two alternative splitting techniques for noninteger v, sampled splitting and expected-value splitting, are compared. Formulas are reported that indicate when each type of splitting is preferred.