Blanchet JH, Liu J. State-dependent importance sampling for regularly varying random walks. Advances in Applied Probability. 2008;40(4):1104-1128. doi:10.1239/aap/1231340166
Abstract
Consider a sequence (Xk: k ≥ 0) of regularly varying independent and identically distributed random variables with mean 0 and finite variance. We develop efficient rare-event simulation methodology associated with large deviation probabilities for the random walk (Sn: n ≥ 0). Our techniques are illustrated by examples, including large deviations for the empirical mean and path-dependent events. In particular, we describe two efficient state-dependent importance sampling algorithms for estimating the tail of Sn in a large deviation regime as n ↗ ∞. The first algorithm takes advantage of large deviation approximations that are used to mimic the zero-variance change of measure. The second algorithm uses a parametric family of changes of measure based on mixtures. Lyapunov-type inequalities are used to appropriately select the mixture parameters in order to guarantee bounded relative error (or efficiency) of the …
Authors: Jose H Blanchet, Jingchen Liu
Publication date: 2008/12
Journal: Advances in Applied Probability
Volume: 40
Issue: 4
Pages: 1104-1128
Publisher: Cambridge University Press
