Journal
THEORY OF PROBABILITY AND ITS APPLICATIONS
Volume 55, Issue 1, Pages 2-26Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0040585X97984632
Keywords
stable distributions; tempered stable distributions; tempered infinitely divisible distributions
Categories
Funding
- Division of Mathematical, Life and Physical Science, College of Letters and Science, University of California, Santa Barbara
- Deutschen Forschungsgemeinschaft
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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 Rosinski [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 Rosinski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric examples.
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