Complete moment convergence of double-indexed randomly weighted sums of mixing sequences
نویسندگان
چکیده
منابع مشابه
State Observers with Random Sampling Times and Convergence Analysis of Double-Indexed and Randomly Weighted Sums of Mixing Processes
Abstract. Algorithms for system identification, estimation, and adaptive control in stochastic systems rely mostly on different types of signal averaging to achieve uncertainty reduction, convergence, stability, and performance enhancement. The core of such algorithms is various types of laws of large numbers that reduce the effect of noises when they are averaged. Many of the noise sequences e...
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The complete moment convergence of weighted sums for arrays of rowwise φ-mixing random variables is investigated. By using moment inequality and truncation method, the sufficient conditions for complete moment convergence of weighted sums for arrays of rowwise φ-mixing random variables are obtained. The results of Ahmed et al. 2002 are complemented. As an application, the complete moment conver...
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Copyright q 2010 Wang Xuejun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Some results on complete convergence for weighted sums ∑n i 1 aniXi are presented, where {Xn, n ≥ 1} is a sequence of φ-mixing random variables an...
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We investigate the complete convergence of partial sums of randomly weighted extended negatively dependent (END) random variables. Some results of complete moment convergence, complete convergence and the strong law of large numbers for this dependent structure are obtained. As an application, we study the convergence of the state observers of linear-time-invariant systems. Our results extend t...
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Let be a sequence of arbitrary random variables with and , for every and be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on and sequence .
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2016
ISSN: 1029-242X
DOI: 10.1186/s13660-016-1260-4