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General conditions for bounded relative error in simulations of highly reliable Markovian systems

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

Published online by Cambridge University Press:  01 July 2016

Marvin K. Nakayama
Marvin K. Nakayama*
Affiliation:
New Jersey Institute of Technology
*
∗ Postal address: Department of Computer and Information Science, New Jersey Institute of Technology, Newark, NJ 07102, USA.
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Abstract

We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating a performance measure of a highly reliable Markovian system. Also, a class of importance sampling methods is defined for which we prove a necessary and sufficient condition for bounded relative error for the performance measure estimator. This class of probability measures includes all of the currently existing failure biasing methods in the literature. Similar conditions for derivative estimators are established.

Keywords

SIMULATIONIMPORTANCE SAMPLINGLIKELIHOOD RATIOSGRADIENT ESTIMATIONRELIABILITYMARKOV CHAINS

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
General Applied Probablity
Information
Advances in Applied Probability , Volume 28 , Issue 3 , September 1996 , pp. 687 - 727
Copyright
Copyright © Applied Probability Trust 1996 

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