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

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