The Strong Limit Theorem Of Sum Of Delay Of Markov Chain And The Application Of Markov Model

In the history of probability theory,the study of strong limit theory has been very important.The strong limit theory of Markov chains has been one of the research contents of many probability theorists.Markov processes are very important in theory and practice,and they are widely used in computer science,life science,calculation methods,economic management and market forecasting.This paper mainly studies the strong limit theorem of Markov chain delay sum and the application of Markov model in stock index prediction.In the theoretical research part of this paper,we first study the generalized strong deviation theorem of nonnegative continuous random variable’s time delay sum function.As a corollary,we get the generalized strong law of numbers of nonnegative continuous random variable’s time delay sum function.Secondly,a class of generalized strong deviation theorems for the sum of time delays of binary functions of arbitrary nvalued random variables is established,and the generalized strong law of numbers and the generalized asymptotic equipartition property for the sum of time delays of nonhomogeneous Markov chain functional functions are given.This paper mainly extends and improves the results of some current literatures,and makes corresponding improvements to the corresponding results of existing literatures.In the application part of this paper,the daily return rate data and closing price data of the CSI 300 stock index are taken as the research object,and the high-order Markov model and the weighted Markov model are respectively used to make shortterm prediction of the CSI 300 stock index.The results show that the rise and fall of the stock index predicted by the last two models are better than the actual value.