Precise large deviations for sums of random vectors with dependent components of consistently varying tails  

作　　者：Xinmei SHEN Yuqing NIU Hailan TIAN 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

出　　处：《Frontiers of Mathematics in China》2017年第3期711-732,共22页中国高等学校学术文摘·数学（英文）

摘　　要：Let {Xi = （X1,i,...,Xm,i）T, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X1 are allowed to be generally dependent. Moreover, let N（.） be a nonnegative integer-valued process, independent of the sequence {Xi, i ≥ 1}. Under several mild assumptions, precise large deviations for Sn =∑i=1 n Xi and SN（t） =∑i=1 N（t） Xi are investigated. Meanwhile, some simulation examples are also given to illustrate the results.Let {Xi = （X1,i,...,Xm,i）T, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X1 are allowed to be generally dependent. Moreover, let N（.） be a nonnegative integer-valued process, independent of the sequence {Xi, i ≥ 1}. Under several mild assumptions, precise large deviations for Sn =∑i=1 n Xi and SN（t） =∑i=1 N（t） Xi are investigated. Meanwhile, some simulation examples are also given to illustrate the results.

关 键 词：Precise large deviations MULTI-DIMENSIONAL consistently varying distributions random sums 

分 类 号：T[一般工业技术]