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 On Complete Convergence for Arrays of Rowwise ρ-Mixing Random Variables and Its Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 769201 12 pages doi 2010 769201 Research Article On Complete Convergence for Arrays of Rowwise p-Mixing Random Variables and Its Applications Xing-cai Zhou1 2 and Jin-guan Lin1 1 Department of Mathematics Southeast University Nanjing 210096 China 2 Department of Mathematics and Computer Science Tongling University Tongling Anhui 244000 China Correspondence should be addressed to Jin-guan Lin jglin@ Received 15 May 2010 Revised 23 August 2010 Accepted 21 October 2010 Academic Editor Soo Hak Sung Copyright 2010 . Zhou and . Lin. 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. We give out a general method to prove the complete convergence for arrays of rowwise p-mixing random variables and to present some results on complete convergence under some suitable conditions. Some results generalize previous known results for rowwise independent random variables. 1. Introduction Let Q F P be a probability space and let Xn n 1 be a sequence of random variables defined on this space. Definition . The sequence Xn n 1 is said to be p-mixing if p ri sup sup k t XeL2 Ff YeL2F k EXY - EXEY ự EX - EXÝEÍY - EY 2 J- - 0 as n where Fm denotes the ơ-field generated by Xg m i n . The p-mixing random variables were first introduced by Kolmogorov and Rozanov 1 . The limiting behavior of p-mixing random variables is very rich for example these in the study by Ibragimov 2 Peligrad 3 and Bradley 4 for central limit theorem Peligrad 5 and Shao 6 7 for weak invariance principle Shao 8 for complete convergence Shao 2 Journal of Inequalities and Applications 9 for almost sure invariance principle Peligrad 10 Shao 11 and Liang and Yang 12 for convergence rate Shao 11 for the maximal inequality and so forth. For .
