On a class of characterization problems for random convex combinations
type: Item
instance of: scholarly article
title: On a class of characterization problems for random convex combinations
zbMATH Open document ID: 0936.60012
DOI: 10.1023/A:1003127114209
author: Ludwig Baringhaus
author: Rudolf Grübel
published in: Annals of the Institute of Statistical Mathematics
publication date: 2000-05-09T00:00:00Z
review text: The authors consider equations of the form \[ X{\overset {d} =}W_1 \cdot X+W_2\cdot X',\tag{1} \] where \(W=(W_1,W_2)\) is a random vector with \(E(W_1+W_2)=1\) and \(X{\overset {d} =}X'\), with \(W,X\) and \(X'\) independent in the right-hand side. Special cases of equations of this type have been considered by several authors. The authors give an existence and uniqueness theorem for solutions of (1) under a moment condition, based on a contraction property and using a special metric. As a very special case they mention a characterization of the exponential distribution related to the total staying time in an M/M/1 queue. There is a result on tail behaviour of the solutions of (1) satisfying a moment condition. Some extensions are mentioned.
reviewed by: Fred W. Steutel
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1310122
zbMATH Keywords: stochastic equation
zbMATH Keywords: characterization problems
zbMATH Keywords: contractions
MaRDI profile type: Publication
full work available at URL: a:1003127114209
OpenAlex ID: W2071578271
description: scientific article; zbMATH DE number 1310122