On a class of probability distributions that is closed with respect to addition as well as multiplication of independent random variables

Date

Jun 19, 2014

Time

2:00 PM - 3:00 PM

Speaker

Prof. Lennart Bondesson

Affiliation

University of Umeå, Sweden

Series

TUD Mathematik AG Analysis & Stochastik

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Dr. Anita Behme

Description

Let P be a class of probability distributions on R_+ = [0, 8). We write X ~ P if the distribution of the random variable X is in P. Problem: Is there a non-trivial P such that a) X ~ P, c > 0 ? cX ~ P; b) X ~ P, Y ~ P (X and Y independent) ? X + Y ~ P; c) X ~ P, Y ~ P (X and Y independent) ? X • Y ~ P d) P is closed with respect to weak limits. Answer: Yes. The most interesting such class is presented. This talk contains in particular a review of the concepts of generalized gamma convolution and hyperbolic complete monotonicity. Open problems are presented. A very new result is mentioned.

Links

• Webseite der AG Analysis & Stochastik

Last modified: Jun 2, 2014, 6:13:07 PM