Strong Limit Theorems For Nonhomogeneous Finite Markov Chains And Applications

Markov process is an important probabilistic process.It has profound theoretic foundation,such as topology,theory of functions, functional analysis,modern algebra and geometry.In addition,it has extensive applied area,such as physics,chemistry,biology,astronomy, computer,communication and management of economy.The research about homogeneous Markov chains has formed integrated theoretic system.The research about limit theorems and ergodic properties has been researching in recent years.This article is going to study limit theorems for finite non-homogeneous Markov chains,calculating entropy rate and forecasting for exchange rate.In the first chapter,we introduce the research and progresses about Markov chains.In the second chapter,we introduce the basic theory which needs to use in the subsequent chapters.In the third chapter,we study limit theorems for finite non-homogeneous Markov chains.Firstly, Yang weiguo and Liu Wen studied the asymptotic equipartition properties for Markov information,based on the uniform integrability of random variable sequences,we are to give limit theorems..As corollary,we obtain the limit properties for entropy density for non-homogeneous Markov.In the fourth chapter,we study the entropy rate of a random walk on a weighted graph,introduce the entropy rate of a chess about china chess,then compare to the freedom of a chess about china chess.In the last chapter,we analyse the type of the exchange rate risk and the judged elements.We forecast for exchange rate with the theory of Markov chains and make a strategic decision with reference to the powerful-weak index.At last,we prove the feasibility and the practicability by force of testing the example.