An Analytical Study on Markov Chain Based on Graph Theory
YU Guo-fang · Journal of Huaiyin Institute of Technology · 2006
This paper makes an analytical study on Markov chain based on graph theory.A concept of probability flux is presented,which is the product of stable state probability and one step transition probability and has influx and efflux forms.A set of balance equations of probability flux is established.That is,when a Markov chain reaches balanced state at a certain time,probability influx is equal to efflux in its every state.The authors compare the balance equations with Kirchoff's current conservation law(KCL),and draw a conclusion that they both have unified formalism.It has a good visualizability and intelligibility to compute the stable state probabilities of Markov chain by the balance equations.