SUPPORTS OF CONVOLUTIONS OF IDENTICAL DISTRIBUTIONS.

Abstract

Simple examples are given of convolutions of identical singular univariate distributions whose convolution is absolutely continuous. Furthermore, it is shown that there exist infinitely divisible univariate distributions F and G such that the Hausdorff dimensions of the supports (lowest-dimensional sets of probability 1) of F(t), G(t), and F(t) * G(t) have any preassigned behavior consistent with non-decrease under convolution. Absolute continuity can be included as a dimension greater than 1. Furthermore, the Levy-Khintchine representations of F and G may be required to be purely discrete or purely signular. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 26, 1965
Accession Number
AD0623863

Entities

People

  • Herman Rubin

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Continuity
  • Convolution

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Regression Analysis.