tailieunhanh - Báo cáo hóa học: " Research Article Moment Inequality for ϕ-Mixing Sequences and Its Applications"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Moment Inequality for ϕ-Mixing Sequences and Its Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 379743 12 pages doi 2009 379743 Research Article Moment Inequality for -Mixing Sequences and Its Applications Wang Xuejun Hu Shuhe Shen Yan and Yang Wenzhi School of Mathematical Science Anhui University Hefei Anhui 230039 China Correspondence should be addressed to Hu Shuhe hushuhe@ Received 11 April 2009 Accepted 21 September 2009 Recommended by Sever Silvestru Dragomir Firstly the maximal inequality for -mixing sequences is given. By using the maximal inequality we study the convergence properties for -mixing sequences. The Hajek-Renyi-type inequality strong law of large numbers strong growth rate and the integrability of supremum for -mixing sequences are obtained. Copyright 2009 Wang Xuejun et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let Xn n 1 be a random variable sequence defined on a fixed probability space Q F P and Sn Xỉ Xi for each n 1. Let n and m be positive integers. Write Fm ơ Xi n i m . Given Ơ-algebras B R in F let q B R sup P B A - P B . AéB BeR P A 0 Define the -mixing coefficients by q n sup VfÍz FTO Jz n 0. k 1 x Definition . A random variable sequence Xn n 1 is said to be a -mixing random variable sequence if qfri ị 0 as n TO. The concept of -mixing random variables was introduced by Dobrushin 1 and many applications have been found. See for example Dobrushin 1 Utev 2 and Chen 3 2 Journal of Inequalities and Applications for central limit theorem Herrndorf 4 and Peligrad 5 for weak invariance principle Sen 6 7 for weak convergence of empirical processes Iosifescu 8 for limit theorem Peligrad 9 for Ibragimov-Iosifescu conjecture Shao 10 for almost sure invariance principles Hu and Wang 11 for large deviations and so forth. When these are .