Coupling methods for efficient simulation of spatial population dynamics

TL;DR

This paper demonstrates how coupling techniques can significantly improve the efficiency of simulating spatial population dynamics, especially for processes with monotonicity, by trading memory for speed.

Contribution

It introduces a basic coupling method applicable to all processes and a specialized variant that greatly accelerates simulations satisfying a monotonicity condition.

Findings

Basic coupling trades memory for speed.

Specialized coupling achieves several orders of magnitude speedup.

Memory increase is modest compared to speed gains.

Abstract

Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe a basic coupling technique, applicable to all kinds of processes, which allows trading memory use for a limited speedup. Next, I describe a specialized variant of it, which can be used to speed up the simulation certain kinds of processes satisfying a monotonicity criterion. This special algorithm increases the speed by several orders of magnitude with only a modest increase in memory usage.