论文标题
$ \ mathbb {z}^d $ - 值分布的无限划分的cramér-
A Cramér--Wold device for infinite divisibility of $\mathbb{Z}^d$-valued distributions
论文作者
论文摘要
We show that a Cramér--Wold device holds for infinite divisibility of $\mathbb{Z}^d$-valued distributions, i.e. that the distribution of a $\mathbb{Z}^d$-valued random vector $X$ is infinitely divisible if and only if $\mathcal{L}(a^T X)$ is infinitely divisible for all $a\in \ Mathbb {r}^d $，而这反过来等同于无限的划分，$ \ mathcal {l}（a^t x）$对于所有$ a \ in \ mathbb {n} _0 _0^d $。证明这一点的关键工具是lévy-khintchine类型表示，并具有符号lévy度量，以$ \ mathbb {z}^d $可估算的分布的特征函数，前提是特征函数不含零。
We show that a Cramér--Wold device holds for infinite divisibility of $\mathbb{Z}^d$-valued distributions, i.e. that the distribution of a $\mathbb{Z}^d$-valued random vector $X$ is infinitely divisible if and only if $\mathcal{L}(a^T X)$ is infinitely divisible for all $a\in \mathbb{R}^d$, and that this in turn is equivalent to infinite divisibility of $\mathcal{L}(a^T X)$ for all $a\in \mathbb{N}_0^d$. A key tool for proving this is a Lévy--Khintchine type representation with a signed Lévy measure for the characteristic function of a $\mathbb{Z}^d$-valued distribution, provided the characteristic function is zero-free.
