Importance sampling for stochastic recurrence equations with heavy tailed increments

Jose Blanchet, Henrik Hult, Kevin Leder

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Importance sampling in the setting of heavy tailed random variables has generally focused on models with additive noise terms. In this work we extend this concept by considering importance sampling for the estimation of rare events in Markov chains of the form X n+1 = A n+1X n+B n+1, X 0 = 0, where the B n's and A n's are independent sequences of independent and identically distributed (i.i.d.) random variables and the B n's are regularly varying and the A n's are suitably light tailed relative to B n. We focus on efficient estimation of the rare event probability P(X n > b) as b↗∞. In particular we present a strongly efficient importance sampling algorithm for estimating these probabilities, and present a numerical example showcasing the strong efficiency.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 Winter Simulation Conference, WSC 2011
Pages3824-3831
Number of pages8
DOIs
StatePublished - 2011
Event2011 Winter Simulation Conference, WSC 2011 - Phoenix, AZ, United States
Duration: Dec 11 2011Dec 14 2011

Publication series

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

Other

Other2011 Winter Simulation Conference, WSC 2011
CountryUnited States
CityPhoenix, AZ
Period12/11/1112/14/11

Fingerprint Dive into the research topics of 'Importance sampling for stochastic recurrence equations with heavy tailed increments'. Together they form a unique fingerprint.

Cite this