## The Annals of Applied Probability

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

### Error analysis of tau-leap simulation methods

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

#### 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