Independent random variables on Abelian groups with independent the sum and difference

G. M. Feldman

Independent random variables on Abelian groups with independent the sum and difference

Probability 2015-10-19 v1

Authors: G. M. Feldman

Abstract

Let X be a second countable locally compact Abelian group. Let $\xi_1, \xi_2$ be independent random variables with values in the group X and distributions $\mu_1, \mu_2$ such that the sum $\xi_1+\xi_2$ and the difference $\xi_1-\xi_2$ are independent. Assuming that the connected component of zero of the group $X$ contains a finite number elements of order 2 we describe the possible distributions $\mu_k$ .

Keywords

Abelian groups independent random variables sum and difference locally compact groups second countable probability distributions elements of order 2

Cite

@article{arxiv.1510.04798,
  title  = {Independent random variables on Abelian groups with independent the sum and difference},
  author = {G. M. Feldman},
  journal= {arXiv preprint arXiv:1510.04798},
  year   = {2015}
}

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