D族END随机变量的随机和的精确大偏差

Precise Large Deviation for Random Sums of END Random Variables with Dominatedly Varying Tails

设{X_i,i≥1}是一列服从控制变化尾分布族(D族)的非负的、END的但不必是同分布的随机变量序列,{N_t,t≥0}是一列取非负正整数值的随机变量序列.在给定一些假设条件下,得到了随机和的S(t)=∑_(i=1)^(N(t))X_i(t≥0)的精确大偏差的结论,推广了独立情形下的相应结论.

Let {Xi, i 〉 1} be a sequence of non-negative and extended negatively dependent （END） but not necessarily identically distributed random variables with dominatedly varying tails （D）, and let {Nt, t 〉 0} be a sequence of nonnegative and integer-valued random variables. Under some assumptions, the result of precise large deviation for random sums S（t） =∑N（t） Xi（t 〉 0） is derived, and some corresponding result of the independent case is extended.