## Assaf Zeevi

*On the inefficiency of state-independent importance sampling in the presence of heavy tails*

Coauthor(s): Achal Bassamboo, Sandeep Juneja.

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**Abstract:**

We consider importance sampling simulation for estimating rare event probabilities in the presence of heavy-tailed distributions that have polynomial-like tails. In particular, we prove
the following negative result: there does not exist an asymptotically optimal *state-independent* change-of-measure for estimating the probability that a random walk (respectively, queue length
for a single server queue) exceeds a "high" threshold before going below zero (respectively, becoming empty). Furthermore, we derive explicit bounds on the best asymptotic variance
reduction achieved by state-independent importance sampling relative to naive simulation. We
illustrate through a simple numerical example that a "good" *state-dependent* change-of-measure
may be developed based on an approximation of the zero-variance measure.

**Source:** *Operations Research Letters*

**Exact Citation:**

Bassamboo, Achal, Sandeep Juneja, and Assaf Zeevi. "On the inefficiency of state-independent importance sampling in the presence of heavy tails." *Operations Research Letters* 35, no. 2 (March 2007): 251-260.

**Volume:** 35

**Number:** 2

**Pages:** 251-260

**Date:**
3
2007