Asymptotic optimality of the cross-entropy method for Markov chain problems

TL;DR

This paper demonstrates that the cross-entropy method is asymptotically optimal for Markov chain rare event simulation under certain conditions, linking it to zero-variance importance sampling.

Contribution

It establishes a theoretical connection between the cross-entropy method and zero-variance estimators, providing conditions for asymptotic optimality in Markov chain problems.

Findings

Cross-entropy method is asymptotically optimal under specific conditions.

Links between cross-entropy and zero-variance importance sampling are established.

Provides theoretical foundation for using cross-entropy in rare event simulation.

Abstract

The correspondence between the cross-entropy method and the zero-variance approximation to simulate a rare event problem in Markov chains is shown. This leads to a sufficient condition that the cross-entropy estimator is asymptotically optimal.