Observation And Statistics About Several Types Of Markov Chain

It is found that all transition rates are uniquely determined via observation and statistics of few states when ionic channel activity,particle system,network model or else can be described by a reversible Markov chain.Thus all the statistical characteristics of the whole model can be obtained.In this paper,the following fundamental models are researched and the corresponding results are provided.Numeric example to illustrate these conclusions, is provided repectively.1.Model of observation and statistics for star-graph branch Markov chain (see Chapter 2)The transition rate matrix is unquely determined by sequences of sojour time and hitting time at the end point of every branch.2.Model of observation and statistics for reversible cyclic Markov chain (see Chapter 3)The transition rate matrix is unquely determined by sequences of sojour time and hitting time at two neibouring states.S.Model of observation and statistics for a special Markov chain (see Chapter 4)The transition rate matrix is unquely determined by sequences of sojour time and hitting time at three states.4.Model of observation and statistics for stratified Markqv chain (see Chapter 5)The transition rate matrix is unquely determined by sequences of sojour time and hitting time at the bottom states.5.On the application of Markov chain Monte Carlo methods to estimating the first eigenvalue of Q-matrix (see Chapter 6)Given a Q-matrix,a reversible Markov chain is constructed. And then we can construct a new reversible Markov chain by appending a state.As a result,its first eigenvalue is estimated by the distribution of the hitting time of the attached state.