A class of small deviation theorems for functionals of random fields on a homogeneous tree |
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Authors: | Weicai Peng Weiguo Yang Bei Wang |
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Institution: | Faculty of Science, Jiangsu University, Zhenjiang, 212013, PR China |
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Abstract: | By constructing a non-negative martingale on a homogeneous tree, a class of small deviation theorems for functionals of random fields, the strong law of large numbers for the frequencies of occurrence of states and ordered couple of states for random fields, and the asymptotic equipartition property (AEP) for finite random fields are established. As corollary, the strong law of large numbers and the AEP for Markov chains indexed by a Cayley tree is obtained. Some known results are generalized in this paper. |
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Keywords: | Small deviation theorems Homogeneous tree Random field Strong law of large numbers |
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