Small and large scale behavior of the Poissonized telecom process
type: Item
instance of: scholarly article
title: Small and large scale behavior of the Poissonized telecom process
zbMATH Open document ID: 1066.60043
DOI: 10.1023/B:MCAP.0000045085.17224.82
author: Serge Cohen
author: Murad S. Taqqu
published in: Methodology and Computing in Applied Probability
publication date: 2005-02-11T00:00:00Z
review text: Let \(Y\left( t\right) =\int_X\int_R\int_R\left( G\left( x,t+u\right) -G\left( x,u\right) \right) w\tilde{N}\left( dx,du,dw\right) \) be the Poissonized mixed moving average, where \(\tilde{N}\) is a compensated Poisson point measure. Conditions are obtained for convergence in distribution of \(\lim_{\rho \rightarrow \infty }\rho ^{-H_{\infty }\left( t\right) }Y\left( \rho t\right) \) to the fractional Brownian motion \(B_{H_{\infty }}\left( t\right).\) In case \(\rho \downarrow 0\), a similar convergence problem is considered for \(\rho ^{-H_{\infty }}\left( Y\left( t_{0}+\rho t\right) -Y\left( t_{0}\right) \right) \) and the limit is the stable mixed moving average. The results are applied both to the standard and the canonical Poissonized telecom processes. Some comments on the difference in the similarity parameter \(H_{\infty }\) of these processes are presented.
reviewed by: Nijolė Kalinauskaitė
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 2133630
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: self-similarity
zbMATH Keywords: local self-similarity
MaRDI profile type: Publication
full work available at URL: b:mcap.0000045085.17224.82
OpenAlex ID: W2046089985
description: scientific article; zbMATH DE number 2133630