A simple proof for the continuity of infinite convolutions of binary random variables (Q1116522)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A simple proof for the continuity of infinite convolutions of binary random variables |
scientific article; zbMATH DE number 4090461
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof for the continuity of infinite convolutions of binary random variables |
scientific article; zbMATH DE number 4090461 |
Statements
A simple proof for the continuity of infinite convolutions of binary random variables (English)
0 references
1989
0 references
Let \(X_ j\), \(j\geq 1\), be independent random variables taking the values \(a_ j\geq b_ j\) with distribution \(p_ j=P(x_ j=a_ j)=1-P(X_ j=b_ j)\). Assume that the infinite series \(U=\Sigma X_ j\) is (a.s.) convergent. We give a simple proof for Lévy's theorem on the continuity of the distribution function F(x) of U.
0 references
binary random variables
0 references
convergence infinite convolution
0 references
continuity of the limiting distribution
0 references
