SIA Matrices and Non-Negative Subdivision
SIA Matrices and Non-Negative Subdivision
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DOI：
10.1007/s00025-012-0289-z
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发表时间：
2012-08
影响因子：
2.2
通讯作者：
K. Jetter;Xianjun Li
中科院分区：
文献类型：
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作者：
K. Jetter;Xianjun Li
利用随机矩阵无穷积在非齐次有限马尔可夫过程中的结果，对非负细分一致收敛的结果进行了修正和推广。基于SIA矩阵和遍历系数的概念，讨论了这类乘积到秩一矩阵的几何收敛性。我们还指出了这些矩阵的有向图的性质。通过这种方式，将现有的非负细分的收敛性结果置于此类过程的背景下。
We reprove and extend results for uniform convergence of non-negative subdivision using results from infinite products of stochastic matrices as they appear in the study of non-homogeneous finite Markov processes. Geometric convergence of such products to rank one matrices, based on the notions of SIA matrices and of the so-called ergodic coefficient, is discussed. We also point to the properties of the directed graphs of such matrices. In this way the existing convergence results for non-negative subdivision are put into the context of such processes.