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

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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.

Original languageEnglish (US)
Pages (from-to)687-727
Number of pages41
JournalAdvances in Applied Probability
Volume28
Issue number3
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

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