# Questions tagged [infinite-divisibility]

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### Uncountable divisible groups and the existence of order-preserving isomorphisms of their subsets

Let $(G,+,0,<)$ be an ordered divisible group of uncountable dimension. Consider the subset $G^{<0}$ of $G$. Question: Are $G$ and $G^{<0}$ isomorphic as ordered sets? Does there exist an ...
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### Infinite divisiblity of log-normals

What is the law of a piece of a log-normal distribution? We know that log-normals are infinitely divisible. What would be the law of a root of log-normal? More specifically, suppose that $X$ is a ...
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### Questions about Levy measure in the canonical representation of infinitely divisible distributions

Let $X$ be a random variable with infinitely divisible and symmetric distribution $F$ distributed on $\mathbb{R}$. It is well known that the characteristic function of $X$ has a canonical ...
I asked this question here In S.E but i don't received any resposnes for it, I would like to know if it is appropriate for M.O. I'm always interesting for properties of the following series : $\... 0answers 80 views ### Boudedness of linear operator between generalized Orlicz spaces I am using the notations, definitions, and results of the Section X of  on generalized Orlicz spaces. We say that$\varphi : \mathbb{R} \rightarrow \mathbb{R}^+$is a$\varphi$-function if it is ... 0answers 237 views ### What is the Blumenthal-Getoor index of Student's distributions? For infinitely divisible random variables, Blumenthal and Getoor introduced in  an index that allow to study for instance the local Hölder regularity of Lévy processes. For a symmetric infinitely ... 1answer 714 views ### Is$n=6$the only integer satisfies${\sigma}_x(n) \equiv 0\bmod{n}$for every odd integer$x > 0$and$2 (\bmod n)$if$x$is even integer? [closed] After a few computations in wolfram alpha about the divisor function for some values of$n$to look the behavior of$\sigma_x(n)\bmod n$for$\,n=6,\,$i got this result :$\sigma_x(6)=0 \bmod 6$for$...
Let $X$ and $Y$ be independent and identically distributed random variables. Can $X+Y$ be a uniform distribution? (Please prove.) In other words, is a uniform distribution divisible? The meaning of "...