高阶多元Markov链联合稳定分布向量的扰动界

发布时间：2018-09-10 14:43

【摘要】：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.
[Abstract]:Some perturbation bounds of the joint stable distribution vector of higher order multivariate Markov chains are given. Combining with the correlation properties of the left and right eigenvectors of the probability transfer matrix of higher order multivariate Markov chains, the perturbation bounds of the joint stable distribution vectors of higher order multivariate Markov chains are obtained. The new perturbation bound result is a generalization of the perturbation bound result of the joint stable distribution vector of the first order multivariate Markov chain, and by using the particularity of the probability transfer matrix of the higher order multivariate Markov chain, the perturbation bound in which the joint stable distribution vector can be calculated is given. It is also a generalization of the corresponding perturbation bounds for the joint stable distribution vector of first-order multivariate Markov chains, combining with the Paz inequality, the component perturbation of the joint stable distribution vector of higher order multivariate Markov chains is analyzed. The perturbation bound of the joint stable distribution vector based on the component form is obtained. It is convenient to observe the perturbation of a particular state of a particular chain in a higher order multivariate Markov chain.
【作者单位】：韶关学院数学与统计学院;华南师范大学数学科学学院;
【基金】：国家自然科学基金项目(11601340) 中山大学广东省计算科学重点实验室开放基金项目(2016005) 广东省数据科学工程技术研究中心开放基金项目(2016KF11) 韶关学院科研项目(S201501018)
【分类号】：O211.62

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