On Boolean selfdecomposable distributions
Takahiro Hasebe, Kei Noba, Noriyoshi Sakuma, Yuki Ueda
Studia Mathematica 274 (2024), 129-151
MSC: Primary 46L54; Secondary 60E07
DOI: 10.4064/sm221227-29-10
Published online: 24 January 2024
Abstract
This paper introduces the class of selfdecomposable distributions concerning Boolean convolution. A general regularity property of Boolean selfdecomposable distributions is established; in particular, the number of atoms is at most 2 and the singular continuous part is 0. We then analyze how shifting probability measures changes Boolean selfdecomposability. Several examples are presented to supplement the above results. Finally, we prove that the standard normal distribution is Boolean selfdecomposable but the shifted one N(m,1) is not for sufficiently large |m|.
Authors
- Takahiro HasebeDepartment of Mathematics
Hokkaido University
Sapporo, 060-0810 Hokkaido, Japan
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- Kei NobaDepartment of Statistical Inference and Mathematics
The Institute of Statistical Mathematics
Tachikawa, 190-8562 Tokyo, Japan
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- Noriyoshi SakumaGraduate School of Natural Sciences
Nagoya City University
Nagoya, 467-8501 Aichi, Japan
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- Yuki UedaDepartment of Mathematics
Hokkaido University of Education
Asahikawa, 070-8621 Hokkaido, Japan
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