| Markov information source as a special source in information theory,and its play an important role for the information theory. Markov information source play an important role in population growth, the real-life service system and on. The relative entropy of information theory also play an important role in group decision problems,image algorithmic and computer systems. However, many practical applications of the source are dual or even multiple, which is necessary to study second Markov information source research. In this paper, the theorem is generalized to the non-homogeneous Markov Chains by using its strong law of large numbers.Firstly,this paper mainly introduced the research background and recent situation in the research of scholars both at home and abroad, and make a simple plan of the concrete structure,and also introduces the concepts, theorems and properties.Then we got and prove a theorems of non-homogeneous Markov Chains.Yang-Weiguo use martingale theorem gives a binary function’s limits theorem of non-homogeneous Markov Chains, Csiszar I proved a limit theorem for random variables in information theory, which the corollary of the theorem is relative entropy.In this paper, the theorem is generalized to the non-homogeneous Markov Chains which is from information theory by using a binary function’s limits theorem of non-homogeneous Markov Chains source.However, in real life we found that, in order to describe a class of practical problems need to use non-homogeneous two- order Markov chains, Yang-Weiguo use martingale theorem gives a function with three variables limits theorem of the source of non-homogeneous Markov Chains. This article will continue to promote the theorem of information theory.What’s more Loève gives a strong limit theorem of a independent random variables sequences in probability theory and Shiryaev generalizes a strong limit theorem of a independent random variables sequences by using Kolmogorov three series theorem,this paper gives a concrete example and through this example shows the theorem which is given by Shiryaev is a new type of theorem.At the end of this paper,the content of this paper are summarized, and pointed out the deficiencies that exist in the research process, and also on the direction of future research brief. |
