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STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE |
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| Authors: | Yang Weiguo Faculty of Science Jiangsu University of Science and Technology Zhenjiang China Hebei University of Technology Tianjin China |
| Institution: | Yang Weiguo Faculty of Science,Jiangsu University of Science and Technology,Zhenjiang 212013,China Hebei University of Technology,Tianjin 300130,China |
| Abstract: | This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied. |
| Keywords: | Cayley tree random field Markov chains field strong law of large numbers Shannon-McMillan theorem |
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