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We study how to sample paths of a random walk up to the first time it crossesa fixed barrier, in the setting where the step sizes are iid with negative meanand have a regularly varying right tail. We introduce a desirable property fora change of measure to be suitable for exact simulation. We study whether thechange of measure of Blanchet and Glynn (2008) satisfies this property and showthat it does so if and only if the tail index $\alpha$ of the right tail liesin the interval $(1, \, 3/2)$.

A Dichotomy for Sampling Barrier-Crossing Events of Random Walks with Regularly Varying Tails