Uniformisation techniques for stochastic simulation of chemical reaction networks

This work considers the method of uniformisation for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformisation can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformisation from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformisation approach forms a computationally attractive choice. Furthermore, as a new application of the uniformisation method, we provide a novel variance reduction method for the estimation of general summary statistics of chemical reaction networks based upon the combination of stratification and uniformisation.