关于非齐次树指标Markov链的一类强大数定律

A Class of Strong Laws of Large Numbers for Markov Chains Indexed by a Non-Homogeneous Tree

关于树指标Markov链,国内外学者对此已经做了许多相关的研究,强大数定律是概率论中的重要问题之一.本文通过引入树指标Markov链相对于乘积对数正态分布滑动相对熵的概念,研究给出了非齐次树上Markov链关于对数正态分布的一类强大数定律.

In recent years, scholars at home and abroad have conducted a lot of related researches on the tree-indexed Markov chains. Strong law of large numbers is one of the most important problems in probability theory. In this paper, by introducing the concept of moving relative entropy of the tree indexed Markov chains relative to product log-normal distribution, a class of strong laws of large numbers of log-normal distribution for Markov chains on a non-homogeneous tree are established.