独立重尾随机变量随机和的大偏差估计

摘要

In this paper, we investigate the precise large deviation for heavy-tailed random sums S(t) N(t) ∑Xk , for t ≥0, where {N(t),t ≥ 0} are non-negative integer-valued random variables, and k=1{Xn, n ≥ 1} , independentof{N(t),t≥0} , are non-negative, independent random variables. Our re-sults extend the classical results under the case that Xn, n ≥ 1 } are independent and identically distributed by extended regular variation.%本文研究了一类独立重尾随机变量随机和S(t) ∑Xk,t≥0的大偏差概率.其中{N(t),t≥0}N(t)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{X,n≥1}为独立同分布情形推广到了独立不同分布情形.