# Weak law of large numbers for linear processes

@article{Characiejus2016WeakLO,
title={Weak law of large numbers for linear processes},
author={Vaidotas Characiejus and Alfredas Ra{\vc}kauskas},
journal={Acta Mathematica Hungarica},
year={2016},
volume={149},
pages={215-232}
}
• Published 1 February 2016
• Mathematics
• Acta Mathematica Hungarica
We establish sufficient conditions for the Marcinkiewicz–Zygmund type weak law of large numbers for a linear process $${\{X_k:k\in\mathbb Z\}}$${Xk:k∈Z} defined by $${X_k=\sum_{j=0}^\infty\psi_j\varepsilon_{k-j}}$$Xk=∑j=0∞ψjεk-j for $${k\in\mathbb Z}$$k∈Z, where $${\{\psi_j:j\in\mathbb Z\}\subset\mathbb R}$${ψj:j∈Z}⊂R and $${\{\varepsilon_k:k\in\mathbb Z\}}$${εk:k∈Z} are independent and identically distributed random variables such that $${{x^p\Pr\{|\varepsilon_0| > x\}\to 0}}$$xpPr{|ε0|>x}→0…
4 Citations
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Communications in Statistics - Theory and Methods
• 2018
Abstract In this paper, we consider convergence rates in the Marcinkiewicz–Zygmund law of the large numbers for the END linear processes with random coefficients. We extend some results of Baum and
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Communications in Statistics - Theory and Methods
• 2021
Abstract In this paper, we investigate the complete convergence and complete moment convergence of asymptotically almost negatively associated random variables with random coefficients. The obtained
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Journal of inequalities and applications
• 2017
This paper extends the result of Baum and Katz to the long-range dependent linear processes and obtains convergence rates in the Marcinkiewicz-Zygmund law of large numbers for short-rangedependent linear processes.

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