Statistical Identification Of Discrete-time Markov Chains With Double-cycle Graph

In this paper Markov chain inversion method and the extended taboo probability are applied to explore the statistical identification of discrete-time reversible double-cycle Markov chains of several different types.This paper is divided into three chapters.Specific arrangements are as follows:In Chapter 1,firstly,the research background and significance of Markov chain are introduced briefly.Secondly,the research status of statistical identification of continuous-time and discrete-time Markov chain are described.Finally,the main research results of this paper are given.In Chapter 2,some basic knowledge and lemmas related to the research of this article are given.Then the definition of the extended taboo probability and the basic properties are introduced.In Chapter 3,the main work is statistical identification study on discretetime reversible Markov chain with double-cycle graph.The following conclusions are obtained:for all discrete-time reversible double-cycle Markov chain,they can be identified by separately observing any pair of adjacent states(that is,four states in total)in the two sub-cycles.In particular,the closer the two adjacent states are to the central state of the sub-cycle,the easier it is to identify the transition probability.For the simplest single-cross-point double-cycle Markov chain,it can be statistically confirmed by only three states(the central state of the double-cycle graph with three degrees and one state adjacent to it in each of the sub-cycles).For the simplest double-cycle chain with a common edge,it can be identified by observing the two states on the common edge.