独立随机变量部分和的大偏差概率的估计

独立随机变量部分和的大偏差概率的估计 ESTIMATES FOR PROBABILITIES OF LARGE DEVIATIONS FOR PARTIAL SUMS OF INDEPENDENT RANDOM VARIABLES 胡亦钧 Hu Yijun 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 设｛Ｘｎ｝ｎ≥１是一列相互独立且具有相同分布、非负非退化的随机变量序列．Ｓ＝Ｘ１＋…＋Ｘｎ，μＥＸ１，ａ是Ｘ１的分布支撑的上确界．假设ＥｅｕＸ１＜∞，ｕ＞０．对μ＜Ｘｎ＜ａ，本文分别讨论了１ｏｇＰ｛Ｓｎ≥ｎｘｎ｝及Ｐ｛Ｓｎ≥ｎｘｎ｝Ｊ当ｎ→∞时的渐近性质。 Let {Xn}n>1, be a sequence of independent,identically distributed,nonnegative nondegenerate random varibles. Let Sn= X1 +… +Xn,n>1,μ= EX1, and a be the supremum of the support of the distribution of X1. Assume Eeux1 for u>0. In this paper,for pM x.Ma, we discuss the asymptotic behavior of logP{Sn>nxn} and P{Sn>nxn} when n→ 大偏差概率 中心极限定理 一致随机紧 large deviations probabilities central limit theorem uniformly random compact O211.5 国家自然科学基金(61672102) 1995-05-01 2021-04-01 5