On importance sampling with mixtures for random walks with heavy tails

2009/09/17 by Henrik Hult, Hult, Henrik, Jens Svensson +1
Computer Science · Decision Sciences · Mathematics · #60G50 #65C05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60G50 #msc:65C05

paper · pdf · doi:10.48550/arxiv.0909.3333

arxiv created 2009/09/17 · openalex publication_date 2009/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Importance sampling algorithms for heavy-tailed random walks are considered. Using a specification with algorithms based on mixtures of the original distribution with some other distribution, sufficient conditions for obtaining bounded relative error are presented. It is proved that mixture algorithms of this kind can achieve asymptotically optimal relative error. Some examples of mixture algorithms are presented, including mixture algorithms using a scaling of the original distribution, and the bounds of the relative errors are calculated. The algorithms are evaluated numerically in a simple setting.

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