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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quasi-infinite divisibility of a class of distributions with discrete part
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by David Berger and Merve Kutlu
Proc. Amer. Math. Soc. 151 (2023), 2211-2224
DOI: https://doi.org/10.1090/proc/16312
Published electronically: February 10, 2023

Abstract:

We consider distributions on $\mathbb {R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its characteristic function is bounded away from zero, thus giving a new class of quasi-infinitely divisible distributions. Moreover, for this class of distributions we characterize the existence of the $g$-moment for certain functions $g$.
References
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Bibliographic Information
  • David Berger
  • Affiliation: Technische Universität Dresden, Institut für Mathematische Stochastik, 01062 Dresden, Germany
  • MR Author ID: 1398889
  • Email: david.berger2@tu-dresden.de
  • Merve Kutlu
  • Affiliation: Universität Ulm, Institut für Finanzmathematik, 89081 Ulm, Germany
  • MR Author ID: 1441249
  • Email: merve.kutlu@live.de
  • Received by editor(s): April 21, 2022
  • Received by editor(s) in revised form: September 13, 2022
  • Published electronically: February 10, 2023
  • Additional Notes: This work was financially supported through the DFG-NCN Beethoven Classic 3 project SCHI419/11-1 & NCN 2018/31/G/ST1/02252.
  • Communicated by: Amarjit Budhiraja
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2211-2224
  • MSC (2020): Primary 60E07, 60E10; Secondary 60E05
  • DOI: https://doi.org/10.1090/proc/16312
  • MathSciNet review: 4556212