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

The paper establishes a necessary condition for any importance sampling scheme to give bounded relative error when estimating a performance measure of a hgihly reliable Markovian system. Also, a class of importance sampling methods is defined for which it proves 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.