关于鞅强大数定律的收敛速度

Pub Date : 2015-03-04 DOI:10.1080/17442508.2014.938075

Y. Miao, Guangyu Yang, G. Stoica

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引用次数: 7

摘要

本文的目的是建立鞅的Marcinkiewicz-Zygmund强数定律中的Baum-Katz型收敛速率，它改进了Stoica[鞅的中等偏差概率系列，J. Math]的最新工作。分析的苹果336(2005)，第759-763页;鞅的Baum-Katz-Nagaev型结果，数学。分析的苹果336 (2007)，pp. 1489-1492;关于鞅强大数定律收敛速度的注解[j]。分析的应用学报，381 (2011)，pp. 910-913]。此外，我们还研究了均匀混合过程的一些相关极限行为。在一些均匀混合条件下，建立了鞅级数收敛的充要条件。

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On the rate of convergence in the strong law of large numbers for martingales

The aim of this note is to establish the Baum–Katz type rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers for martingales, which improves the recent works of Stoica [Series of moderate deviation probabilities for martingales, J. Math. Anal. Appl. 336 (2005), pp. 759–763; Baum–Katz–Nagaev type results for martingales, J. Math. Anal. Appl. 336 (2007), pp. 1489–1492; A note on the rate of convergence in the strong law of large numbers for martingales, J. Math. Anal. Appl. 381 (2011), pp. 910–913]. Furthermore, we also study some relevant limit behaviours for the uniform mixing process. Under some uniform mixing conditions, the sufficient and necessary condition of the convergence of the martingale series is established.

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