高阶多元Markov链联合稳定分布向量的扰动界

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

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 one-order 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.