  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.
