The Annals of Applied Probability

Error analysis of tau-leap simulation methods

David F. Anderson, Arnab Ganguly, and Thomas G. Kurtz

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 6 (2011), 2226-2262.

Dates
First available in Project Euclid: 23 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1322057321

Digital Object Identifier
doi:10.1214/10-AAP756

Mathematical Reviews number (MathSciNet)
MR2895415

Zentralblatt MATH identifier
1234.60066

Subjects
Primary: 60H35: Computational methods for stochastic equations [See also 65C30] 65C99: None of the above, but in this section
Secondary: 92C40: Biochemistry, molecular biology

Keywords
Tau-leaping simulation error analysis reaction networks Markov chain chemical master equation

Citation

Anderson, David F.; Ganguly, Arnab; Kurtz, Thomas G. Error analysis of tau-leap simulation methods. Ann. Appl. Probab. 21 (2011), no. 6, 2226--2262. doi:10.1214/10-AAP756. https://projecteuclid.org/euclid.aoap/1322057321


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References

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