tailieunhanh - Báo cáo hóa học: " Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables Aiting Shen"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables Aiting Shen | Shen Journal of Inequalities and Applications 2011 2011 93 http content 2011 1 93 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables Aiting Shen Correspondence baret@ School of Mathematical Science Anhui University Hefei 230039 China Springer Abstract In this article the strong limit theorems for arrays of rowwise negatively orthant-dependent random variables are studied. Some sufficient conditions for strong law of large numbers for an array of rowwise negatively orthant-dependent random variables without assumptions of identical distribution and stochastic domination are presented. As an application the Chung-type strong law of large numbers for arrays of rowwise negatively orthant-dependent random variables is obtained. MR 2000 Subject Classification 60F15 Keywords negatively orthant-dependent sequence array of rowwise negatively orthant-dependent random variables strong law of large numbers 1 Introduction Let Xn n 1 be a sequence of random variables defined on a fixed probability space F P with value in a real space R. We say that the sequence Xn n 1 satisfies the strong law of large numbers if there exist some increasing sequence an n 1 and some sequence cn n 1 such that 1 n ỵ Xi Ci 0 . as n x. an i 1 Many authors have extended the strong law of large numbers for sequences of random variables to the case of triangular array of random variables and arrays of rowwise random variables. For more details about the strong law of large numbers for triangular array of random variables and arrays of rowwise random variables one can refer to Gut 1 and so forth. In the case of independence Hu and Taylor 2 proved the following strong law of large numbers. Theorem . Let Xni 1 i n n 1 be a triangular array of rowwise independent random variables. Let an n 1 be a sequence of positive real .