Convergence rates for probabilities of moderate deviations for moving average processes |
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| Authors: | Ping Yan Chen Ding Cheng Wang |
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| Institution: | (1) Department of Mathematics, Jinan University, Guangzhou, 510630, P. R. China;(2) Center of Financial Mathematics, MSI, Australian National University, Canberra, Act 0200, Australia;(3) School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China |
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| Abstract: | The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined
results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the
sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence)
for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some
well-known results.
Chen’s work is supported by National Natural Science Foundation of China (Grant No. 60574002), and Wang’s work is supported
by MASCOS grant from Australian Research Council and National Natural Science Foundation of China (Grant No. 70671018) |
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| Keywords: | complete convergence complete moment convergence moderate deviation law of the iterated logarithm invariance principle moving average process |
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