馬氏鏈及樹上馬氏鏈場的若干極限定理.pdf

1、河北工業(yè)大學碩士學位論文馬氏鏈及樹上馬氏鏈場的若干極限定理姓名：蘭景濤申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：金少華20070601E ' , S 3 ? E ' , ; b ? ? O z l ?SOME LIMIT THEOREMSOF MARKOV CHAINSAND MARKOV CHAIN FIELDS ON TREESABSTRACTMarkov processes is an important rand

2、om processes,it has not only pro-found theoretic foundament but also extensive applied area.The researchof strong limit theorem is always one of central subjects in internationalprobability fields.This paper used marting

3、ale convergence theorem by con-structing proper martingale to study some limit theorems of Markov chainand Markov chain fields on trees.This paper includes six chapters. The first chapter is introduc-tion,introducing bac

4、kground of choosing the subject in this paper and thework that existed.The chapters from the second to the fifth are main parts.In the second chapter, a strong limit theorem of the three variables functionof non-homogene

5、ous hidden Markov model is given.In the third chapter, in-troducing strong law of large numbers of Markov chain fields taking valuesin numerable states on generalized Bethe trees. In the fourth chapter, in-troducing a st

6、rong limit theorem of the frequencies of occurrence of statesabout continuous function defined in fixed interval for the Markov chainfields on generalized Cayley trees.The fifth chapter gives main conclusionsof this pape