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September 2012 On exact sampling of nonnegative infinitely divisible random variables
Zhiyi Chi
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Adv. in Appl. Probab. 44(3): 842-873 (September 2012). DOI: 10.1239/aap/1346955267

Abstract

Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on Xr can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

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Zhiyi Chi. "On exact sampling of nonnegative infinitely divisible random variables." Adv. in Appl. Probab. 44 (3) 842 - 873, September 2012. https://doi.org/10.1239/aap/1346955267

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 1261.60023
MathSciNet: MR3024612
Digital Object Identifier: 10.1239/aap/1346955267

Subjects:
Primary: 60E07
Secondary: 60G50

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 3 • September 2012
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