Cayley树图上奇偶马氏链场的渐近均分割性

Asymptotic Equipartition Property for Even-Odd Markov Chain Fields on a Cayley Tree

本文的目的是要研究Cayley树图上奇偶马氏链场的渐近均分割性．首先我们给出Cayley树图上奇偶马氏链场关于状态和状态序偶出现频率的强大数定律,然后证明其具有a.e.收敛性的渐近均分割性．

In this paper, we study the asymptotic equipartition property for even-odd Markov chain fields on a Cayley tree. We first give strong law of large numbers on the frequencies of states and ordered state couples for even-odd Markov chain fields on a Cayley tree, then prove the asymptotic equipartition property for even-odd Markov chain fields on a Cayley tree with a.e. convergence.