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Tau-leaping is a family of algorithms for the approximate simulation of thediscrete state continuous time Markov chains. Motivation for the development ofsuch methods can be found, for instance, in the fields of chemical kinetics andsystems biology. It is known that the dynamical behavior of biochemical systemsis often intrinsically stiff representing a serious challenge for theirnumerical approximation. The naive extension of stiff deterministic solvers tostochastic integration often yields numerical solutions with eitherimpractically large relaxation times or incorrectly resolved covariance. Inthis paper, we propose a splitting heuristic which helps to resolve some ofthese issues. The proposed integrator contains a number of unknown parameterswhich are estimated for each particular problem from the moment equations ofthe corresponding linearized system. We show that this method is able toreproduce the exact mean and variance of the linear scalar test equation anddemonstrates a good accuracy for the arbitrarily stiff systems at least in thelinear case. The numerical examples for both linear and nonlinear systems arealso provided and the obtained results confirm the efficiency of the consideredsplitting approach.

Slow-scale split-step tau-leap method for stiff stochastic chemical systems