Ӧ�ø���ͳ�� 2012, 28(2) 181-188 DOI:      ISSN: 1001-4268 CN: 31-1256

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Strong Convergence Laws for $\wt{\varphi}$-Mixing
Sequences of Random Variables
Huang Haiwu,Wang Dingcheng,Wu Qunying
School of Mathematics Science, University of Electronic Science and Technology of China, College of Science, Guilin University of
Technology, Institute of Financial Engineering, School of Finance, School of Applied Mathematics, Nanjing Audit University,
Abstract:

In this paper, the almost sure convergence
and complete convergence for $\wt{\varphi}$-mixing random variables
are established. The results obtained not only extend and generalize
the classical Khintchine-Kolmogorov Convergence Theorem, the Three
Series Theorem for independent random variables to the case of
$\wt{\varphi}$-mixing random variables, but also improve the
relevant results without necessarily adding any extra any
conditions.

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