Limit theorems for multiplicative processes
type: Item
instance of: scholarly article
title: Limit theorems for multiplicative processes
zbMATH Open document ID: 1039.60035
author: Emmanuel Rio
author: Alain Rouault
author: Quansheng Liu
published in: Journal of Theoretical Probability
publication date: 2004-03-15T00:00:00Z
review text: Let \(W\) be a random variable such that \(W\geq 0\), \(EW= 1\), and let \(\{W_{i_1\cdots i_n}\}\) be a family of independent copies of \(W\), indexed by all finite sequences \(i_1\cdots i_n\) of positive integers. For fixed \(r\) and \(n\) the random multiplicative measure \(\mu^n_r\) has, on each \(r\)-adic interval \(A^r_{i_1\cdots i_n}\) at \(n\)th level, the density \(W_{i_1}\cdots W_{i_1\cdots i_n}\) on \([0,1]\). For each fixed \(1\leq n\leq\infty\) the asymptotic properties (uniform law of large numbers, functional central limit theorem, large deviation principle) for the sequence of random measures \(\{\mu^n_r\}\) are studied as \(r\to\infty\).
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 2057328
zbMATH Keywords: self-similar cascades
zbMATH Keywords: Mandelbrot's martingales
zbMATH Keywords: random measures
zbMATH Keywords: laws of large numbers
zbMATH Keywords: functional central limit theorems
zbMATH Keywords: functional law of the iterated logarithm
zbMATH Keywords: large deviations
reviewed by: Nikolai N. Leonenko
MaRDI profile type: Publication
full work available at URL: b:jotp.0000012003.49768.f6
OpenAlex ID: W2073935264
DOI: 10.1023/B:JOTP.0000012003.49768.F6
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description: scientific article; zbMATH DE number 2057328