 
Summary: Submitted to the Annals of Applied Probability
arXiv: math.PR/0909.4790
ERROR ANALYSIS OF TAULEAP SIMULATION METHODS
BY DAVID F. ANDERSON ARNAB GANGULY AND THOMAS G. KURTZ
University of Wisconsin  Madison
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 com
pare the accuracy of different approximation methods and, specifically, Euler
tauleaping and midpoint tauleaping. We perform our analysis under a scal
ing 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 tauleaping
achieves a higher order of accuracy, in both a weak and a strong sense, than
Euler tauleaping; a result that is in contrast to previous analyses. We present
examples that demonstrate our findings.
1. Introduction. This paper provides an error analysis for numerical approximation methods for con
tinuous time Markov chain models that are becoming increasingly common in the chemistry and biochem
