Strong Limit Theorems For Nonhomogeneous Finite Markov Chains And Applications

Markov process is an important stochastic process. It has profound the-oretic foundation, such as topology, theory of functions, functional analy-sis, modern algebra and geometry. In addition, it has extensive applied area, such as physics, chemistry, biology,astronomy,computer,communication and man-agement of economy. The research about homogeneous Markov chains has formed integrated theoretic system. The research about limit theorems and ergodic propertieshas been researching in recent years. This article is going to study limit theorems for finite non-homogeneous Markov chains, in addi-tion, forecasting for exchang rate with the theory of Markov chains.In the first part,we introduce the research and progresses about Markov chains. In the second part, 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 liuwen stud-ied the asymptotic equipartition properties for Markov information, based on the uniform integrability of random variable sequences, we are to give limit theorems. In the last part, 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 in-dex. At last, we prove the feasibility and the practicability by force of testing and example.