# 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} }

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

### Convergence rates in the law of large numbers for END linear processes with random coefficients

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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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### Convergence rates in the law of large numbers for long-range dependent linear processes

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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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