数学物理学报(英文版)

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LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

胡亦钧; 明瑞星; 杨文权   

  1. 武汉大学数学与统计学院, 武汉 430072
  • 收稿日期:2003-12-15 修回日期:2005-06-15 出版日期:2007-10-20 发布日期:2007-10-20
  • 通讯作者: 胡亦钧
  • 基金资助:

    Partly supported by the National Natural Science Foundation of China and the Ministry of Education of China; Partly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,
    Jianghan University

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

Hu Yijun; Ming Ruixing; Yang Wenquan   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2003-12-15 Revised:2005-06-15 Online:2007-10-20 Published:2007-10-20
  • Contact: Hu Yijun

摘要:

M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large
deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.

关键词: negatively associated random variables, stationary sequence, strong law of large numbers, large deviations, moderate deviations

Abstract:

M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large
deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.

Key words: negatively associated random variables, stationary sequence, strong law of large numbers, large deviations, moderate deviations

中图分类号: 

  • 60F15