Statistical Identification Of Reversible Markov Chain With Cyclic Graph

In the traditional theory of Markov chain,we often assume that transition rate matrix of Markov chain is known,but in realistic systems,the density matrix of a Markov chain might be unknown,and how to determine the density matrix Q is the main task in generally.It is known that for the reversible continuous time markov chain on finite state,its density matrix determine the transition probability matrix.Thus the confirmation of the Q matrix of this markov chain determine the kinetic property of the whole chain.Therefore,we can obtain the Q matrix by observing the motion of some states in the model and utilizing markov chain inversion method.Based on the study of statistical confirmation of Markov chains on tree topology,in this paper,the problem of statistical identification of reversible markov chain with cyclic topology is studied,the general conclusion and the corresponding algorithm are given,and the correctness of the algorithm is verified by a numerical example.