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

• Published in: Acta Mathematica Scientia Vol. 27; no. 4; pp. 886 - 896
• Main Author: 胡亦钧 明瑞星 杨文权
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2007; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China%School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; Department of Mathematics, Jianghan University, Wuhan 430056, China
• Subjects: large deviations; moderate deviations; negatively associated random variables; stationary sequence; strong law of large numbers; 中离差; 固定序列; 大离差; 随机变量; large deviations; negatively associated random variables; strong law of large numbers; stationary sequence; moderate deviations
• ISSN: 0252-9602; 1572-9087; 1003-3998
• DOI: 10.1016/S0252-9602(07)60086-1

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.