大马尔科夫链单一输入超状态分解的择优准则与增效使用

A CRITERION FOR SELECTING OPTIMUM AND A USAGE FOR RAISING EFFICIENCY ON THE SINGLE INPUT SUPERSTATE DECOMPOSITION OF LARGE MARKOV CHAINS

为了计算大马尔科夫链（简记为ＬＭＣ）的平稳分布，ＦｅｉｎｂｅｒｇＢ．Ｎ．和ＣｈｉｕＳ．Ｓ．在文献［１］中提出了单一输入超状态可分解马尔科夫链（简记为ＳＩＳＤＭＣ）的概念，以及切实可行的相应方法为了更加有效地应用此法，本文首先合理地提出了一种优化分解的识别准则，进而深入地探讨了如何确定优良分解中的超状态与其所含状态的个数问题，以及如何根据ＬＭＣ的具体结构建立一种可以简化节省计算的改进方法的问题文中证明所得的结论解决了文献［２］提出的一些问题。

In order to calculate stationary distributions of large Markov Chains (LMC),in literature Feinberg,B.N.and Chiu,S.S.presented the concept of single input superstate decomposable Markov Chains (SISDMC) and a feasible corresponding method.Aiming at applying this method more effectively,first this paper puts forward a criterion for distinguishing majorization decompositions rationally,then explores further problems on how to determine numbers of superstates and states contained by respective superstates in good decompositions,and how to establish an improved method to reduce computing capacity according to the concrete structure of LMC. In this paper,some of problems left over by literature is resolved,and several guided suggestions using the SISD method to raise efficiency is put forward.