基于图论的马尔可夫链分析研究

利用图论对马尔可夫链进行了分析研究,提出了概率通量概念,它是马尔可夫链稳定状态概率与其一步转移概率之乘积,有流入、流出之分;建立了马尔可夫概率通量平衡方程,即一个马尔可夫链经过一定时间达到平衡状态,其每一状态之流入、流出概率通量相等,并将其与电路中的克希荷夫电流守恒定律(KCL)作了对比,二者在形式上是统一的。利用概率通量平衡方程求解马尔可夫链稳定状态概率具有较好的直观性,易于理解。

An Analytical Study on Markov Chain Based on Graph Theory

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.