一类马氏链的解及其数据仿真与应用

A class of Markov chains for solutions and data simulation and application

利用马尔可夫链的几个重要定理,研究了一颗粒在具有n个顶点的正多面体的顶点上运动的转移概率矩阵,得到概率转移矩阵极限中的元素均为,利用定理2求得该颗粒首次返回起跳点所需的平均步数为n,以及该颗粒在首次返回起跳点经过体对顶点的平均次数为1,最后针对一个正八面体,利用计算机随机生成数据进行模拟,得到的结果与定理相吻合的。最后应用该方法研究了生产结构优化的问题。

Use Markov chain and its history of the development and the theorem. Study a particle movement on the Vertex of an n -Vertex polyhedron＇transition probability matrix, and culmulate the probability to be the limit of the transfer matrix elements are 1/n. Use of theorem 2 find the average number of steps that the particles return to the starting point for the first time is n, as well as the particle in return for the first time after take - off point for point - average number is 1. The last for a octa- hedron, randomly generated by computer simulation data, to be The results coincide with the theorem, which further verified the correctness of the theorem. At last use this study the problem of optimizing the production structure.