Random difference equations with logarithmic distribution and the triggered shot noise
type: Item
instance of: scholarly article
title: Random difference equations with logarithmic distribution and the triggered shot noise
zbMATH Open document ID: 1015.60035
DOI: 10.1016/S0196-8858(02)00026-X
published in: Advances in Applied Mathematics
publication date: 2003-04-03T00:00:00Z
review text: The limit in law of the sequence of random variables \(U_n\), \(n \geq 1\), such that \(U_0=0\), \(U_n=X_n (Y_n+U_{n-1})\), \(n\geq 1\), where \(X_i\) are i.i.d. random variables with density \(-\ln x\) on \([0,1]\) or \((-1/2)\ln x\) on \([-1,1]\), is studied. The authors consider the following five cases of distribution: deterministic, binary, Laplace, normal and Cauchy. The presented method may also be used for estimation of the suitable stationary densities.
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60F25
zbMATH DE Number: 1892336
zbMATH Keywords: Poisson process
zbMATH Keywords: shot noise
zbMATH Keywords: Fourier transform
zbMATH Keywords: Tauber's theorem
zbMATH Keywords: integral equation
author: Jean-François Chamayou
author: Jean-Louis Dunau
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
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full work available at URL: s0196-8858(02)00026-x
OpenAlex ID: W2085250314
description: scientific article; zbMATH DE number 1892336