Graduation Year

Spring 2013

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Mark Huber

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© 2013 Robert Tristan Williams

Abstract

This paper focuses on the issue of sampling directly from the stationary distribution of Vervaat perpetuities. It improves upon an algorithm for perfect sampling first presented by Fill & Huber by implementing both a faster multigamma coupler and a moving value of Xmax to increase the chance of unification. For beta = 1 we are able to reduce the expected steps for a sample by 22%, and at just beta = 3 we lower the expected time by over 80%. These improvements allow us to sample in reasonable time from perpetuities with much higher values of beta than was previously possible.

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