Anticorrelated discrete-time stochastic simulation

We provide the first known rigorous theoretical analysis of previously published anticorrelated variance reduction techniques for tau-leaping systems. These algorithms provide a way to reduce the expected MSE of mean estimators by introducing local negative correlation between Monte Carlo sample paths. We prove a recursive equation governing the evolution of these covariances in both the nonlinear and linear cases. Further, we prove sufficient algebraic conditions for variance reduction in the linear rates case that require no stochastic simulation. Finally, we present an example system to illustrate both the application of these tests and to demonstrate their effectiveness.