Tempered infinitely divisible distributions and processes

M. L. Bianchi, S. T. Rachev, Y. S. Kim, F. J. Fabozzi

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36 Scopus citations


In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced in the seminal work of Rosi ́nski [Stochastic Process. Appl., 117 (2007), pp. 677-707], a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosínski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric examples.

Original languageEnglish
Pages (from-to)2-26
Number of pages25
JournalTheory of Probability and its Applications
Issue number1
StatePublished - 2011


  • Stable distributions
  • Tempered infinitely divisible distributions
  • Tempered stable distributions


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