Mathematics – Probability
Scientific paper
2009-09-25
Annals of Applied Probability 2011, Vol. 21, No. 6, 2226-2262
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/10-AAP756 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/10-AAP756
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of the system. We argue that this is a more appropriate scaling than that found in previous error analyses in which the size of the time discretization goes to zero independent of the rest of the model. Under the present scaling, we show that midpoint tau-leaping achieves a higher order of accuracy, in both a weak and a strong sense, than Euler tau-leaping; a result that is in contrast to previous analyses. We present examples that demonstrate our findings.
Anderson David F.
Ganguly Arnab
Kurtz Thomas G.
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