We consider the problem of simulation-based estimation of performance measures for a Markov chain conditioned on a rare event. The conditional law depends on the solution of a multiplicative Poisson equation. An adaptive scheme for learning the latter is proposed and analyzed. An example motivated by a well known problem in communication networks is given. Applications of the basic scheme to other related domains such as importance sampling for rare event simulation and the solution of a class of eigenvalue problems are also sketched.
"Peformance Analysis Conditioned on Rare Events: An Adaptive Simulation Scheme." Commun. Inf. Syst. 3 (4) 259 - 278, 2003.