Arithmetic of a certain semigroup of probability distributions on the group ℝ× ℤ(2)

2023/12/14 by Feldman, Gennadiy
#60B15 (Primary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2312.08637

Abstract

We consider a certain convolution semigroup Θ of probability distributions on the group ℝ× ℤ(2), where ℝ is the group of real numbers and ℤ(2) is the additive group of the integers modulo 2. This semigroup appeared in connection with the study of a characterization problem of mathematical statistics on a-adic solenoids containing an element of order 2. We answer the questions that arise in the study of arithmetic of the semigroup Θ. Namely, we describe the class of infinitely divisible distributions, the class of indecomposable distributions, and the class of distributions which have no indecomposable factors.

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