Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Submitted to the Annals of Applied Probability arXiv: math.PR/0909.4790
 

Summary: Submitted to the Annals of Applied Probability
arXiv: math.PR/0909.4790
ERROR ANALYSIS OF TAU-LEAP 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
tau-leaping and midpoint tau-leaping. 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 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.
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-

  

Source: Anderson, David F. - Department of Mathematics, University of Wisconsin at Madison
Kurtz, Tom - Departments of Mathematics & Statistics, University of Wisconsin at Madison

 

Collections: Mathematics