Random difference equations: An asymptotical result
type: Item
instance of: scholarly article
title: Random difference equations: An asymptotical result
zbMATH Open document ID: 1016.60029
DOI: 10.1016/S0377-0427(02)00821-X
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-22T00:00:00Z
review text: Let \(X_i\) \((i\geq 1)\) be i.i.d. random variables with values in \([0,1]\) and density \(\alpha x^{\alpha-1}\) for some \(\alpha>0\). The authors prove that the recursively defined random variables \(U_n\) with \(U_1=X_1\) and \(U_n=X_n (1+U_{n-1})\) converge in distribution with an explicit limit distribution. Applications to pseudorandom numbers and shot noise are also discussed.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1915273
zbMATH Keywords: central limit theorem
zbMATH Keywords: stochastic difference equation
zbMATH Keywords: Dickman distribution
zbMATH Keywords: pseudorandom numbers
author: Jean-François Chamayou
author: Jean-Louis Dunau
reviewed by: Michael Voit
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00821-x
OpenAlex ID: W2154675796
description: scientific article; zbMATH DE number 1915273