PA序列的Hájek-Rényi型不等式及强大数定律(英文)
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摘要
本文给出了零均值PA序列的一个新的Hájek-Rényi型不等式,该不等式推广了文献[9]中的结果.此外,本文还得到了零均值PA序列的一个Brunk-Prokhorov型强大数定律.
In this paper, a new Hájek-Rényi-type inequality for mean zero associated random variables is obtained, which generalizes and improves the result of Theorem 2.2 of [9]. In addition,a Brunk-Prokhorov-type strong law of large numbers is also given.
In this paper, a new Hájek-Rényi-type inequality for mean zero associated random variables is obtained, which generalizes and improves the result of Theorem 2.2 of [9]. In addition,a Brunk-Prokhorov-type strong law of large numbers is also given.
引文
[1]ESARY J D,PROSCHAN F,WALKUP D W.Association of random variables,with applications[J].Ann Math Stati^st,1967,38(5):1466-1474.
[2]HAJEK J,RENYI A.Generalization of an inequality of Kolmogorov[J].Acta Math Acad Sci Hung,1955,6(3-4):281-283.
[3]GAN S X.The Hájek-Renyi inequality for Banach space valued martingales and the p smoothness of Banach spaces[J].Statist Probab Lett,1997,32(3):245-248.
[4]LIU J J,GAN S X,CHEN P Y.The Hajek-Renyi inequality for the NA random variables and its application[J].Statist Probab Lett,1999,43(1):99-105.
[5]FAZEKAS I,KLESOV O.A general approach to the strong law of large numbers[J].Theory Probab Appl,2001,45(3):436-449.
[6]YANG W Z,SHEN Y,HU S H,et al.Hájek-Rényi-type inequality and strong law of large numbers for some dependent sequences[J].Acta Math Sinica,2012,28(3):495-504.
[7]PRAKASA RAO B L S.Hajek-Renyi-type inequality for associated sequences[J].Statist Probab Lett,2002,57(2):139-143.
[8]SUNG S H.A note on the Hájek-R6nyi inequality for associated random variables[J].Statist Probab Lett,2008,78(7):885-889.
[9]HU S H,WANG X J,YANG W Z,et al.The Hájek-Rényi-type inequality for associated random variables[J].Statist Probab Lett,2009,79(7):884-888.
[10]NEWMAN C M,WRIGHT A L.Associated random variables and martingale inequalities[J].Z Wahrsch Verw Gebiete,1982,59(3):361-371.
[11]CHRISTOFIDES T C.Maximal inequalities for demimartingales and a strong law of large numbers[J].Statist Probab Lett,2000,50(4):357-363.
[12]WANG J F.Maximal inequalities for associated random variables and demimartingales[J].Statist Probab Lett,2004,66(3):347-354.
[13]HU S H,CHEN G J,WANG X J.On extending the Brunk-Prokhorov strong law of large numbers for martingale differences[J].Statist Probab Lett,2008,78(18):3187-3194.
[2]HAJEK J,RENYI A.Generalization of an inequality of Kolmogorov[J].Acta Math Acad Sci Hung,1955,6(3-4):281-283.
[3]GAN S X.The Hájek-Renyi inequality for Banach space valued martingales and the p smoothness of Banach spaces[J].Statist Probab Lett,1997,32(3):245-248.
[4]LIU J J,GAN S X,CHEN P Y.The Hajek-Renyi inequality for the NA random variables and its application[J].Statist Probab Lett,1999,43(1):99-105.
[5]FAZEKAS I,KLESOV O.A general approach to the strong law of large numbers[J].Theory Probab Appl,2001,45(3):436-449.
[6]YANG W Z,SHEN Y,HU S H,et al.Hájek-Rényi-type inequality and strong law of large numbers for some dependent sequences[J].Acta Math Sinica,2012,28(3):495-504.
[7]PRAKASA RAO B L S.Hajek-Renyi-type inequality for associated sequences[J].Statist Probab Lett,2002,57(2):139-143.
[8]SUNG S H.A note on the Hájek-R6nyi inequality for associated random variables[J].Statist Probab Lett,2008,78(7):885-889.
[9]HU S H,WANG X J,YANG W Z,et al.The Hájek-Rényi-type inequality for associated random variables[J].Statist Probab Lett,2009,79(7):884-888.
[10]NEWMAN C M,WRIGHT A L.Associated random variables and martingale inequalities[J].Z Wahrsch Verw Gebiete,1982,59(3):361-371.
[11]CHRISTOFIDES T C.Maximal inequalities for demimartingales and a strong law of large numbers[J].Statist Probab Lett,2000,50(4):357-363.
[12]WANG J F.Maximal inequalities for associated random variables and demimartingales[J].Statist Probab Lett,2004,66(3):347-354.
[13]HU S H,CHEN G J,WANG X J.On extending the Brunk-Prokhorov strong law of large numbers for martingale differences[J].Statist Probab Lett,2008,78(18):3187-3194.