Efficient Computation of Transient Solutions of the Chemical Master Equation Based on Uniformization and Quasi-Monte Carlo

Andreas Hellander

October 2007

Abstract:

A Quasi-Monte Carlo method for the simulation of discrete time Markov chains is applied to the simulation of biochemical reaction networks. The continuous process is formulated as a discrete chain subordinate to a Poisson process using the method of uniformization. It is shown that a substantial reduction of the number of trajectories that is required for an accurate estimation of the probability density functions (PDF) can be achieved with this technique. The method is applied to the simulation of two model problems. Although the technique employed here does not address the typical stiffness of such systems, it is useful when computing the PDF by replication and the method can be used in conjuncture with hybrid methods that reduce the stiffness.

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