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Limiting behaviour of moving average processes under negative association assumption


Authors: P. Chen, T.-C. Hu and A. Volodin
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal: Theor. Probability and Math. Statist. 77 (2008), 165-176
MSC (2000): Primary 60F15
DOI: https://doi.org/10.1090/S0094-9000-09-00755-8
Published electronically: January 21, 2009
MathSciNet review: 2432780
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Abstract: Let $ \{Y_i, -\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed negatively associated random variables, and $ \{a_i, -\infty<i<\infty\}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and complete moment convergence of the maximum partial sums of moving average processes $ \bigl\{\sum^\infty_{i=-\infty} a_i Y_{i+n}, n\geq1\bigr\}$. We improve the results of Baek et al. (2003) and Li and Zhang (2005).


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Additional Information

P. Chen
Affiliation: Department of Mathematics, Jinan University, Guangzhou, 510630, People’s Republic of China
Email: chenpingyan@yahoo.com.cn

T.-C. Hu
Affiliation: Department of Mathematics, National Tsing Hua University Hsinchu 300, Taiwan, Republic of China
Email: tchu@math.nthu.edu.tw

A. Volodin
Affiliation: Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, S4S0A2, Canada
Email: andrei@math.uregina.ca

DOI: https://doi.org/10.1090/S0094-9000-09-00755-8
Keywords: Complete convergence, complete moment convergence, moving average, negative association
Received by editor(s): August 18, 2006
Published electronically: January 21, 2009
Additional Notes: The research of P. Chen was supported by the National Natural Science Foundation of China
The research of T.-C. Hu was partially supported by the National Science Council
The research of A. Volodin was partially supported by the National Sciences and Engineering Research Council of Canada
Article copyright: © Copyright 2009 American Mathematical Society

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