Slow-scale split-step tau-leap method for stiff stochastic chemical systems
It addresses the challenge of simulating stiff stochastic chemical systems, which is important for chemical kinetics and systems biology, but the method is incremental as it extends existing tau-leaping with a splitting heuristic and parameter estimation.
The paper proposes a slow-scale split-step tau-leap method for stiff stochastic chemical systems, which reproduces exact mean and variance for linear scalar test equations and shows good accuracy for stiff systems, with numerical examples confirming efficiency.
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided and the obtained results confirm the efficiency of the considered splitting approach.