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arXiv · 2206.04932

On Boolean selfdecomposable distributions

Takahiro Hasebe·Kei Noba·Noriyoshi Sakuma·Yuki Ueda
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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 two and the singular continuous part is zero. 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 $N(0,1)$ is Boolean selfdecomposable but the shifted one $N(m,1)$ is not for sufficiently large $|m|$.

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Takahiro Hasebe, Kei Noba, Noriyoshi Sakuma, Yuki Ueda. 2022-06-10. On Boolean selfdecomposable distributions. https://arxiv.org/abs/2206.04932

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