Moving Average Random Sequence Of Strong Deviation Theorems And Applications

In the late1970s, when scholars like Liu Wen, etc. studies the Expansion of Real Numbers and Strong Laws of Large Numbers for Markov Chain, they proposed an analysis method totally different from the traditional one; that is, by introducing logarithmic likelihood ratio about distribution of the product as a measurement for differences of the random variable sequence in a comparatively independent condition. In this way, the strong limit theorem of probability theory is generalized to the expression of inequation, building a new theorem—strong deviation theorem.By this method, Professor Wang Zhizhong and Yang Weiguo studied the almost sure nature of random sequence and moving average, proposed the concepts of the random sequence moving likelihood ratio and gradual logarithmic interaction likelihood ratio, taking them as the random measurement of the difference of random sequence and reference distribution of the product. In this way, the part of second order of random sequence and strong deviation theorem of moving average are given.In the identical distribution condition, the author studies the part of N-order random sequence and the strong deviation theorem of moving average.This study tries to continue this question, getting and promoting the result of Professor Wang Zhizhong and Yang Weiguo.First, the part of third order random sequence and strong deviation theorem of moving average are studied and proved, without the requirement of identical distribution, promoting the result of Professor Wang Zhizhong and Yang Weiguo.Then, this paper proves that the part of second order random sequence and strong deviation theorem of moving average can be applied to the interpretation model of sheep-flock effect, giving the exact number of the effect and meanwhile, outreaching and deepening the model itself.