Importance sampling simulation in the presence of heavy tails

Achal Bassamboo, Sandeep Juneja, Assaf Zeevi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 importance sampling relative to naïve 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.

Original languageEnglish
Title of host publicationProceedings of the 2005 Winter Simulation Conference
Pages664-671
Number of pages8
DOIs
StatePublished - 2005
Externally publishedYes
Event2005 Winter Simulation Conference - Orlando, FL, United States
Duration: 4 Dec 20057 Dec 2005

Publication series

NameProceedings - Winter Simulation Conference
Volume2005
ISSN (Print)0891-7736

Conference

Conference2005 Winter Simulation Conference
Country/TerritoryUnited States
CityOrlando, FL
Period4/12/057/12/05

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