给出了高阶多元Markov链联合稳定分布向量的几个扰动界:结合高阶多元Markov链概率转移矩阵左、右特征向量的相关性质,得到高阶多元Markov链联合稳定分布向量的扰动界,新的扰动界结果是一阶多元Markov链联合稳定分布向量扰动界结果的推广;利用高阶多元Markov链概率转移矩阵的特殊性,给出其联合稳定分布向量可计算形式的扰动界,也是已有一阶多元Markov链联合稳定分布向量相应扰动界结果的推广;结合Paz不等式,通过分析高阶多元Markov链联合稳定分布向量的分量扰动,得到了联合稳定分布向量基于分量形式的扰动界,便于观察高阶多元Markov链中具体某条链某个状态的扰动.
The perturbation bounds of the joint stationary distribution vector of the high-order multivariate Markov chains are established.By the properties of the left and right eigenvectors of the probability transition matrix of the high-order multivariate Markov chains,the perturbation bound of the joint stationary distribution vector of the high-order multivariate Markov chains is obtained,which generalizes the results of the existing perturbation bounds of the joint stationary distribution vector of one-order multivariate Markov chains.Then the computational perturbation bound is given by the characteristic of the probability transition matrix of the high-order multivariate Markov chains,which also generalizes the corresponding perturbation bound of the joint stationary distribution vector of oneorder multivariate Markov chains.Moreover,considering the perturbation in the item of the joint stationary distribution vector of high-order multivariate Markov chains,the perturbation bound of the joint stationary distribution vector based on component form is established by Paz's inequality,to observe the perturbation of a state in a chain of the high-order multivariate Markov chains.