计算大马尔科夫链的平稳分布的聚集状态方法

Some Methods for Computing stationary distributions Of large Markov Chains by Aggregating States

计算大马尔科夫链的平稳分布是一个涉及到在庞大实际系统中的应用、理论分析、具体计算等各方面的综合课题。本文综述研究这一课题的基本思想,以及行之有效的新近算法:包括聚集/解除聚集迭代法、替换过程逼近法、单一输入超状态分解法,及其理论依据,最后还提出了若干尚待解决的问题。

This paper surveys basic thought and effective recent algorithms for computing stationary distributions of large Markov chains. Methods involved include (1)the iterative ag-gregation/disaggregation algorithm; (2)the replacement process approach; (3)the single - input superstate decomposable iterative algorithm, and their theoretical basis. Finally, the paper presents problems to be considered further.