Arithmetic of a certain convolution semigroup of probability distributions on the group ℝ × ℤ(2)
We consider a certain convolution semigroup $\Theta$ of probability distribu-tions on the group $\mathbb{R}\times \mathbb{Z}(2)$, where $\mathbb{R}$ is the group of real numbers and $\mathbb{Z}(2)$ is the additive group of the integers modulo 2. This semigroup appeared in connection with the study o...
Gespeichert in:
| Datum: | 2024 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
|
| Schlagworte: | |
| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1084 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Institution
Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | We consider a certain convolution semigroup $\Theta$ of probability distribu-tions on the group $\mathbb{R}\times \mathbb{Z}(2)$, where $\mathbb{R}$ is the group of real numbers and $\mathbb{Z}(2)$ 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 $\boldsymbol{a}$-adic solenoids containing an element of order 2. We answer the questions that arise in the study of arithmetic of the semigroup $\Theta$. Namely, we describe the class of infinitely divisible distributions, the class of indecomposable distributions, and the class of distributions which have no indecomposable factors.
Mathematical Subject Classification 2020: 60B15 |
|---|