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Questions tagged [infinite-divisibility]

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2
votes
1answer
196 views

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 ...
3
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0answers
199 views

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 : $ \...
3
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0answers
73 views

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 ...
3
votes
1answer
91 views

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 ...
0
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2answers
397 views

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 "...
7
votes
1answer
644 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?

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 $...
2
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0answers
176 views

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 ...