In this paper we give an elementary and unified proof of the Hajek-Renyi inequality, and get a general version of this inequality which not only covers the all known results but also derives some new results.
In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences a...In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.展开更多
Abstract In this paper, we get the H^jek-R^nyi-type inequalities for a pairwise NQD sequence, an L^T （r 〉 1） mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong l...Abstract In this paper, we get the H^jek-R^nyi-type inequalities for a pairwise NQD sequence, an L^T （r 〉 1） mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for L^T（r 〉 1） mixingale of Hansen.展开更多
基金Supported by the National Natural Science Foundation of China(10671149)
文摘In this paper we give an elementary and unified proof of the Hajek-Renyi inequality, and get a general version of this inequality which not only covers the all known results but also derives some new results.
基金The NSF(10871001,60803059) of ChinaTalents Youth Fund(2010SQRL016ZD) of Anhi Province Universities+2 种基金Youth Science Research Fund(2009QN011A) of Anhui UniversityProvincial Natural Science Research Project of Anhui Colleges(KJ2010A005)Academic innovation team of Anhui University (KJTD001B)
文摘In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.
基金Supported by the National Natural Science Foundation of China (No. 11171001, 11126176)Natural Science Foundation of Anhui Province (No. 1208085QA03)Provincial Natural Science Research Project of Anhui Colleges (No. KJ2010A005)
文摘Abstract In this paper, we get the H^jek-R^nyi-type inequalities for a pairwise NQD sequence, an L^T （r 〉 1） mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for L^T（r 〉 1） mixingale of Hansen.
