On Boolean selfdecomposable distributions
Volume 274 / 2024
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 $N(0,1)$ is Boolean selfdecomposable but the shifted one $N(m,1)$ is not for sufficiently large $|m|$.
