GENERAL CONDITIONS FOR BOUNDED RELATIVE ERROR IN SIMULATIONS OF HIGHLY RELIABLE MARKOVIAN SYSTEMS

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