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Bounded normal approximation in simulations of highly reliable Markovian systems

Part of: Special processes Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Bruno Tuffin
Bruno Tuffin*
Affiliation:
IRISA-INRIA
*
∗Postal address: IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France. Email address: btuffin@irisa.fr.
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Abstract

In this paper, we give necessary and sufficient conditions to ensure the validity of confidence intervals, based on the central limit theorem, in simulations of highly reliable Markovian systems. We resort to simulations because of the frequently huge state space in practical systems. So far the literature has focused on the property of bounded relative error. In this paper we focus on ‘bounded normal approximation’ which asserts that the approximation of the normal law, suggested by the central limit theorem, does not deteriorate as the reliability of the system increases. Here we see that the set of systems with bounded normal approximation is (strictly) included in the set of systems with bounded relative error.

Keywords

Simulationnormal approximationMarkov chainshighly reliable systems

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 974 - 986
Copyright
Copyright © Applied Probability Trust 1999 

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