Ӧ�ø���ͳ�� 2010, 26(6) 589-596 DOI:      ISSN: 1001-4268 CN: 31-1256

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Strong Limit Theorems for Even-Odd Markov Chain Fields Indexed by Bethe Tree and Cayley Tree
Ma Lina,Chen Shuang
Tianjin University of Commerce,Beijing Institute of Petrochemical Technology
Abstract:

In this article, we propose the definition of the
even-odd Markov chain fields indexed by Bethe tree $T_{B,N}$ (Cayley
tree $T_{C,N}$). A strong limit theorem for the random variable
sequence is proved by constructing two nonnegative martingales, and
then a strong limit theorem for the even-odd Markov chain fields is
obtained with application of the foregoing theorem. As its
corollaries, we gain some strong limit theorems and coarse estimates
for the frequencies of occurrence of states and ordered couples of
states. Thus we generalize parts of strong limit theorems for Markov
chain fields indexed by Bethe trees $T_{B,N}$ and Cayley tree
$T_{C,N}$ and even-odd Markov chain fields indexed by Cayley tree
$T_{C,2}$

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