重尾平稳序列的大偏差

本文给出了一类重尾的随机变量序列{Xn,n≥1}的部分和Sn=∑i=1 n Xi与随机和S(t)=∑i=1^N(t) Xi的大偏差结果其中{N(t),t≥)}是一族非负整值的随机变量，{Xn,n≥1}是非负的平稳过程，并且与{N(t),t≥0}独立。本文将独立同分布情形的结果掖到了平稳相依的情形。

LARGE DEVIATIONS FOR A HEAVY-TAILED STATIONARY SEQUENCE

let {X. ,n≥1} be a stationary sequence of non-negative random variables with the tail of distribution is of Pareto's type (regularly or extended regularly varying), we investigate large deviation for the partial sums Sn=∑ni=1 Xi and the tandom aums S(t) = ∑N(1)i=1 Xi , where {N(t),t ≥ 0} is a process of non-negative integer-valued random variables, independent of {Xn, n ≥ 1}. Some existing results are generalized.