Convergence of weighted sums of random variables with long-range dependence.
type: Item
instance of: scholarly article
title: Convergence of weighted sums of random variables with long-range dependence.
zbMATH Open document ID: 1047.60018
DOI: 10.1016/S0304-4149(00)00040-5
author: Vladas Pipiras
author: Murad S. Taqqu
published in: Stochastic Processes and their Applications
publication date: 2004-09-22T00:00:00Z
review text: Sufficient conditions for the convergence in distribution \[ \frac {1}{m^H}\sum _{n=-\infty }^{\infty }f\left(\frac {n}{m}\right)\xi _n \to \int _{\mathbb R} f(u) dB_H(u), \quad m\to \infty , \] are given where \(f\) is a deterministic function, \(\{\xi _n\}_{n\in \mathbb Z}\) is a sequence of random variables with long-range dependence and \(B_H\) denotes the fractional Brownian motion with the Hurst parameter \(H\in (\frac {1}{2}, 1)\). Two applications are given, the first one concerning the asymptotic behaviour of Weierstrass-Mandelbrot process and the second one coming from the ``moving average'' representation of the fractional Brownian motion with another Hurst parameter \(H'\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 2102346
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: long-range dependence
zbMATH Keywords: Weierstrass-Mandelbrot process
MaRDI profile type: Publication
cites work: Q3738326
cites work: Q5560061
cites work: Q4726487
cites work: The Invariance Principle for Stationary Processes
cites work: Functional limit theorems for weighted sums of i.i.d. random variables
cites work: Weighted sums of i.i.d. random variables attracted to integrals of stable processes
cites work: Q4740120
cites work: Convergence of the Weierstrass-Mandelbrot process to fractional Brownian motion
cites work: Integration questions related to fractional Brownian motion
cites work: Q4945270
cites work: Q3141895
cites work: Q4301585
cites work: Weak convergence to fractional brownian motion and to the rosenblatt process
full work available at URL: s0304-4149(00)00040-5
OpenAlex ID: W2014964957
Recommended article: Convergence of Weighted Sums of Products of Random Variables with Long-Range Dependence
Recommended article: Q3124998
Recommended article: CONVERGENCE OF WEIGHTED SUMS FOR DEPENDENT RANDOM VARIABLES
Recommended article: Convergence of weighted sums of independent random variables
Recommended article: Convergence for weighted sums of widely orthant dependent random variables
Recommended article: On the complete convergence of weighted sums for dependent random variables
Recommended article: A note on convergence of weighted sums of random variables
Recommended article: On the strong convergence of weighted sums of widely dependent random variables
Recommended article: On the strong convergence for weighted sums of random variables
description: scientific article; zbMATH DE number 2102346