术语“更新定理”的详细信息

英译术语:

renewal theorem

汉语语境:

基本更新定理表明，若Xi（i≥1）为同分布的正值独立随机变量列，随机变量Nt=inf∶n∶t <∑nk=1Xk>，那么有ENt→1EX1，t→∞。我们注意到这里独立性是一个很强的条件，我们将以使用性更广泛的负、正相关性来代替独立性这个条件，来获得一些类似结果。

英语语境:

The renewal theorem gives us such a result that if Xi (i≥1)are positive independent random variables with an identical distribution, and random variable Nt=inf:n:t<∑nk=1Xk, then ENt→1EX1, t→∞.We notice that in this theorem independence is a strong condition. We'll substitute for it with negative and positive association, which are used more widely, so as to acquire some similar results.