关于鞅强大数定律的收敛速度

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Stochastics-An International Journal of Probability and Stochastic Processes 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.