正常返Markov链的几乎处处中心极限定理

Almost sure central limit theory for positive recurrent Markov chain

本文考虑不可约正常返Markov链,证明其函数的部分和的几乎处处中心极限定理,把独立同分布(independent and identically distributed,i.i.d.)随机变量序列的几乎处处中心极限定理推广到Markov链,且扩大了使定理成立的权重.

Consider an irreducible and positive recurrent Markov chain. A universal result in almost sure limit central theorem for the partial sums of its function is established. Our results realize the extension of almost sure central limit theorem for a sequence of independent and identically distributed （i.i.d.） random variables to Markov chain.