SENSITIVITY OF THE STATIONARY DISTRIBUTION VECTOR FOR AN ERGODIC MARKOV-CHAIN
SENSITIVITY OF THE STATIONARY DISTRIBUTION VECTOR FOR AN ERGODIC MARKOV-CHAIN
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DOI：
10.1016/0024-3795(86)90210-7
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发表时间：
1986-04-01
影响因子：
1.1
通讯作者：
MEYER, CD
中科院分区：
文献类型：
--
作者：
FUNDERLIC, RE;MEYER, CD
带有转移矩阵的马尔可夫链的平稳分布向量sp ∞在数学科学中的许多模型的分析中是重要的，如排队网络、投入产出经济模型和分区示踪分析模型。本文的目的是提供洞察力的灵敏度p ∞的扰动的转移概率T和理解的一些困难，在计算一个accuratep∞。I-T的群逆A #在理解p ∞的灵敏度或条件方面具有根本的重要性。主要结果表明，如果存在一个状态可以从其它状态到达，且T的相应列没有小的非对角元，则p ∞对T中的小扰动不敏感.本文提出了一种计算A #的新算法。
Stationary distribution vectorsp∞for Markov chains with associated transition matricesTare important in the analysis of many models in the mathematical sciences, such as queuing networks, input-output economic models, and compartmental tracer analysis models. The purpose of this paper is to provide insight into the sensitivity ofp∞to perturbations in the transition probabilities ofTand to understand some of the difficulties in computing an accuratep∞. The group inverseA#ofI−Tis shown to be of fundamental importance in understanding sensitivity or conditioning ofp∞. The main result shows that if there is a state that is accessible from every other state and the corresponding column ofThas no small off-diagonal elements, thenp∞cannot be sensitive to small perturbations inT. Ecological examples are given. A new algorithm for calculatingA#is described.