独立重尾随机变量随机和的大偏差估计(英文)

AN ESTIMATE OF LARGE DEVIATIONS FOR HEAVY-TAILED RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES

本文研究了一类独立重尾随机变量随机和S(t) ∑N(t)k=1Xk ,t≥ 0的大偏差概率 .其中 {N(t) ,t≥ 0 }是一族非负整数值随机变量 ;{Xn,n≥ 1}是非负、独立随机变量序列 ,并与 {N(t) ,t≥ 0 }独立 .本文的结果将{Xn,n≥ 1}为独立同分布情形推广到了独立不同分布情形 .

In this paper, we investigate the precise large deviation for heavy-tailed random sums S(t)∑N(t)k=1X k, for t≥0, where {N(t),t≥0} are non-negative integer-valued random variables, and {X n, n≥1} , independent of {N(t),t≥0}, are non-negative, independent random variables. Our results extend the classical results under the case that {X n, n≥1} are independent and identically distributed by extended regular variation.