剩余寿命的若干极限性质

设非负随机变量T₁,T₂,…,T_n,…独立同分布,分布函数F为连续,而{N(t),t ≥ 0}是以T₁,T₂,…为相继到达时间而产生的更新计数过程.本文求出了当t ≥ 0,s ≥ 0时,剩余寿命γ(t)与γ(t+s)的联合分布函数以及其混合矩当t,s→∞时的极限性态.结果表明t,s→∞时,γ(t)和γ(t+s)是渐近独立的.

SOME LIMIT PROPERTIES OF EXCESS LIFE

The paper is devoted to the study of excess life in renewal process. It is proved in the paper that the excess life γ(t) and γ(t+s) at time t and t+s respectively are asymptotically independent. And it is also shown that the mixed moment Eγ^m(t) γⁿ(t+s) equals asymptotically to the product of the limits lim_t→∞ Eγ^m(t) and lim_t→∞ Eγⁿ(s).