Efficient simulation of discrete stochastic reaction systems with a splitting method
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Stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error.
KeywordsStochastic simulation algorithm Discrete stochastic reaction systems Splitting methods Analytic solution formulas Error bounds Chemical master equation
Mathematics Subject Classification (2000)60J75 65L70 47D06 92D25 92C42
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- 1.Alfonsi, A., Cancès, E., Turinici, G., Ventura, B.D., Huisinga, W.: Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. In: ESAIM: Proc., vol. 14, pp. 1–13 (2005) Google Scholar
- 2.Anderson, D.F., Ganguly, A., Kurtz, T.G.: Error analysis of tau-leap simulation methods. Ann. Appl. Probab. (2010, to appear). arXiv:0909.4790v2 [math.PR]
- 3.Banasiak, J.: A complete description of dynamics generated by birth-and-death problem: a semigroup approach. In: Rudnicki, R. (ed.) Mathematical Modelling of Population Dynamics. Collection of Papers from the Conference, Będlewo, Poland, June 24–28, 2002. Banach Center Publications, vol. 63, pp. 165–176 . Polish Academy of Sciences, Institute of Mathematics, Warsaw (2004) Google Scholar
- 4.Burrage, K., Tian, T.: Poisson Runge-Kutta methods for chemical reaction systems. In: Sun, Y.L.W., Tang, T. (eds.) Advances in Scientific Computing and Applications, pp. 82–96. Science Press, Beijing (2004) Google Scholar
- 13.Engblom, S.: Numerical Solution Methods in Stochastic Chemical Kinetics. PhD thesis, Uppsala University (2008) Google Scholar
- 16.Gibson, M.A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104(9), 1876–1889 (2000) Google Scholar
- 26.Hegland, M.: Approximating the solution of the chemical master equation by aggregation. In: Mercer, G.N., Roberts, A.J. (eds.) Proceedings of the 14th Biennial Computational Techniques and Applications Conference, CTAC-2008, ANZIAM J. 50, C371–C384 (2008) Google Scholar
- 29.Jahnke, T.: Splittingverfahren für Schrödingergleichungen. Wiss. Arbeit für das Staatsexamen, Universität Tübingen, Germany (1999) Google Scholar