N 值随机变量序列的 AEP 型极限及若干强偏差定理

AEP-like Limit and Some Strong Deviation Theorems for N-valued Random Variables

设｛Ｘｎ，ｎ≥１｝是在Ｓ＝｛１，２，…，Ｎ｝中取值的随机变量序列，其分布为ｐ（ｘ１，…，ｘｎ）．ｌｉｍｉｎｆｎ〔ｐ（Ｘ１，…，Ｘｎ）〕１／ｎ与ｌｉｍｓｕｐｎ〔ｐ（Ｘ１，…，Ｘｎ）〕１／ｎ称为ＡＥＰ型极限，利用这些极限得到｛Ｘｎ，ｎ≥１｝的若干强偏差定理，即一类用不等式表示的强极限定理．

let {X n,n≥1}be a sequence of random variables taking values in S={1,2,…,N} with the joint distribution p(x 1,…,x n). liminf n p(X 1,…,X n 1/n and limsup n p(x 1,…,x n 1/n are called the AEP-like limits. In virtue of these limits ,Some strong deviation theorems,namely a class of strong limit theorems represented by inequalities are obtained .