关于图值随机元序列的若干强极限定理

On Some Limit Theorems for Sequence of Graph-Valued Random Elements

设{ξ_i}_(i=1)~∞是一列独立同分布在图Γ=(V(Γ),E(Γ))上取值的随机元,{a_i}_(i=1)~∞是一列固定的正整数.文章给出图值随机元序列的r-阶权函数、r-阶均值集与r-阶中心序等概念,将随机元序列的Fréchet样本均值的概念推广到更一般的情形,并且讨论了其基本性质,获得了关于图值随机元序列的广义强大数定理.

Let {ξi}∞i=1 be a sequence of independent identically distributed random elements taking values on a graph Г=（V（Г）,E（Г））, {ai}∞i=1 be a sequence of fixed positive integers. In this paper, we first give the definitions of general rth weight function, r-th order mean set and r-th cental order of random elements. Then, we extend the Fr6chet mean of random elements to more generalized cases and discuss some basic properties of them. Fklrthermore, we prove a general strong law of large numbers for graph-valued random elements.