Analysis of Explicit Tau-Leaping Schemes for Simulating Chemically Reacting Systems

This paper builds a convergence analysis of explicit tau-leaping schemes for simulating chemical reactions from the viewpoint of stochastic differential equations. Mathematically, the chemical reaction process is a pure jump process on a lattice with state-dependent intensity. The stochastic differential equation form of the chemical master equation can be given via Poisson random measures. Based on this form, different types of tau-leaping schemes can be proposed. In order to make the problem well-posed, a modified explicit tau-leaping scheme is considered. It is shown that the mean square strong convergence is of order 1/2 and the weak convergence is of order 1 for this modified scheme. The novelty of the analysis is to handle the non-Lipschitz property of the coefficients and jumps on the integer lattice.