关于混合序列函数的弱不变原理的一点注解

作者在〔1〕中已对混合序列函数的弱不变原理作了讨论,虽然不对混合系数速度作任何假设,但对矩所加的条件比较苛刻,并且很难验证.本文利用〔2〕中的方法,把文〔1〕定理2中的条件(B)更换成通常所要求的Lindeberg条件,这样我们所得到的结论就包含了许多已知的结果,例如〔3〕中定理21.1,〔4〕中定理4.2.另外〔1〕中定理6条件(F)也不易验证,本文则给出了条件(F)成立的简单明了的充分条件.

A Note On Weak Invariance Principles for Functions of Mixing Processes

In this note we use the same symbols as in the section 21 of the book (Billingsley, 1968). The main results are the following. Theorem 1. Let be a-mixing and lim Suppose that (A) (B) (C) Then if and lim inf we have Theorem 2. Let be mixing. Suppese that (A) and (C) hold, and (D) sup for some (E) Then we have