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On exact sampling of nonnegative infinitely divisible random variables. (English) Zbl 1261.60023
The author explains how a rather wide range of nonnegative infinitely divisible random variables, which are specified by Lévy measures, can be sampled exactly. The main result can be described as follows: for any nonnegative infinitely divisible random variable $$X$$ of a specified Lévy measure, if its distribution conditional on $$X\leq r$$ 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 $$X$$. The suggested procedure does not rely on explicit approximations to distributions, complements other available sampling procedures and, mainly, enables exact sampling of nonnegative infinitely divisible random variables with Lévy measures having infinite integrals on $$(0,\infty)$$.

##### MSC:
 60E07 Infinitely divisible distributions; stable distributions 62D05 Sampling theory, sample surveys
##### Keywords:
infinitely divisible; rejection sampling; exact sampling
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