Convergence of weighted sums of random variables with long-range dependence.

DOI10.1016/S0304-4149(00)00040-5zbMath1047.60018OpenAlexW2014964957MaRDI QIDQ1879488

Murad S. Taqqu, Vladas Pipiras

Publication date: 22 September 2004

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(00)00040-5

zbMATH Keywords

fractional Brownian motionlong-range dependenceWeierstrass-Mandelbrot process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic integrals (60H05) Self-similar stochastic processes (60G18)

Related Items (7)

Tempered Hermite process ⋮ Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with ghp noise ⋮ Asymptotic theory for regression models with fractional local to unity root errors ⋮ On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data ⋮ Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem ⋮ Analysis of the Rosenblatt process ⋮ Limit theorems for weighted sums of infinite variance random variables attracted to integrals of linear fractional stable motions

Cites Work

• Functional limit theorems for weighted sums of i.i.d. random variables
• Weighted sums of i.i.d. random variables attracted to integrals of stable processes
• Integration questions related to fractional Brownian motion
• CONVERGENCE OF THE WEIERSTRASS-MANDELBROT PROCESS TO FRACTIONAL BROWNIAN MOTION
• Weak convergence to fractional brownian motion and to the rosenblatt process
• The Invariance Principle for Stationary Processes
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