Jose Blanchet, Henrik Hult, and Kevin Leder. 2013. Rare-event simulation for stochastic recurrence equations with heavy-tailed innovations. ACM Trans. Model. Comput. Simul. 23, 4, Article 22 (October 2013), 25 pages. https://doi.org/10.1145/2517451

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Abstract

In this article, rare-event simulation for stochastic recurrence equations of the form

Xn+1=An+1Xn+Bn+1, X0=0

is studied, where {An;n≥ 1} and {Bn;n≥ 1} are independent sequences consisting of independent and identically distributed real-valued random variables. It is assumed that the tail of the distribution of B1 is regularly varying, whereas the distribution of A1 has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as P{Xn>b} and P{supk≤nXk > b} for large b and n is studied. Importance sampling strategies are investigated that provide unbiased estimators with bounded relative error as b and n tend to infinity.

Authors
Jose Blanchet, Henrik Hult, Kevin Leder
Publication date
2013/12/16
Journal
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Volume
23
Issue
4
Pages
1-25
Publisher
ACM