Deviation Theorems Of Function Of Two Variables Of Arbitrary Information Sources And Transformation Of Laplace And The Study Of Mutual Information

The strong deviation theorems are new type theorems established by using the notion of the likelihood ratio .Professor Liu Wen frist applied an analysis method in solving a class of strong deviation theorems for a sequense of random variables.Later Professor Liu Wen studied the Shannon-McMillan theorem in information theorems[2]-[8] and deviation theorems of non-negative continuous random variables[10]-[11]by using the analytic technique and obtained some strong deviation theorems .The chapter 2 of the paper studied a class of strong deviation theorems of function of two variables of information sources and obtained a further study of Shannon-McMillan theorem of Markov information sourses by definning the using concept of Entropy Density Divergence.The chapter 3 of the paper studied a class of strong deviation theorems of non-negative continuous random variables by using tool of transformation of Laplace.Information theory ,as a branch of applied probability theory,becomes more and more important in appling. Toru Tsujishita have given a class of theory about triple mutual information by studing information theory. On the basis of the theory,the chapter 4 of the paper studied the proposition of mutual information between two variables and the third variable as the same time it studied further the proposition of mutual information between n variables and the (n+l)th variable .