Deviation Theoremes Of The Multivariate Function Sequences Of Arbitrary Random Variables

Professor Liu Wen, who first invented analysis method in solving Large Number theorem, connected it with moment generating functions, conditional moment generating functions and differentiation of measures on a net, and some strong limit theorems are obtained. This paper continue to study and expand these results. By using conditional moment generating functions and differentiation of measures on a net, some limit theorems and a class of deviation theorems of multivariate function sequences of arbitrary random variables ralated to the conditional expectations are obtained. They are extensions of the limit properties for nonhomogeneous Markov chains, gambling systems, and the harmonic mean of random conditional probablities. A strong deviation theorem of multivariate function sequences of arbitrary random variables is obtained by using moment generating functions and differentiation of measures on a net. And a strong deviation theorem of discrete information sources is obtained.