# Questions tagged [infinite-divisibility]

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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 ...

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### Any counter example for this: ${\phi(2^n-1)} \bmod \tau(2^n-1)=0$ for every integer $n \geq 1$? [closed]

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 : $ \...

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### Boudedness of linear operator between generalized Orlicz spaces

I am using the notations, definitions, and results of the Section X of [1] on generalized Orlicz spaces.
We say that $\varphi : \mathbb{R} \rightarrow \mathbb{R}^+$ is a $\varphi$-function if it is ...

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### Uncountable divisible groups and the existence of order-preserving ismorphisms of their subsetss

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 exists an ...

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### divisibility of uniform distribution [closed]

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 "...

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### 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?

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 $...

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### What is the Blumenthal-Getoor index of Student's distributions?

For infinitely divisible random variables, Blumenthal and Getoor introduced in [1] an index that allow to study for instance the local Hölder regularity of Lévy processes.
For a symmetric infinitely ...