We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy...

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this...

We consider level crossing for the difference of independent renewal processes. Second-order expansions for the distribution function of the crossing time of level n are found, as n -- [infinity]. As a by-product several other results on the difference process are found. The expected minimum of...