A New Family of Mappings of Infinitely Divisible Distributions Related to the Goldie – Steutel – Bondesson Class

@inproceedings{Aoyama2009ANF,
title={A New Family of Mappings of Infinitely Divisible Distributions Related to the Goldie – Steutel – Bondesson Class},
author={Takahiro Aoyama and Alexander M. Maller Lindner and Makoto Maejima},
year={2009}
}

Let {X t } be a Lévy process on R whose distribution at time 1 is a d-dimensional infinitely distribution μ. It is known that the set of all infinitely divisible distributions on R, each of which is represented by the law of a stochastic integral ∫ 1 0 log 1 t dX (μ) t for some infinitely divisible distribution on R, coincides with the Goldie-Steutel-Bondesson class, which, in one dimension, is the smallest class that contains all mixtures of exponential distributions and is closed under… CONTINUE READING

The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

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