Eigentime identity for transient Markov chains
Eigentime identity for transient Markov chains
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DOI：
10.1016/j.jmaa.2005.04.068
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发表时间：
2006-03
影响因子：
1.3
通讯作者：
Y. Mao
中科院分区：
文献类型：
--
作者：
Y. Mao
证明了瞬时对称化马氏链的一个本征恒等式。对于一般马氏链，如果Green矩阵的迹是有限的，则第一跳时的期望是一致有界的，并且证明了对于单生过程，这两种期望是等价的。对于生灭过程，给出了显式公式。作为应用，我们给出了从L∞到L∞的(子)马氏半群Pt的指数收敛速度的界。
An eigentime identity is proved for transient symmetrizable Markov chains. For general Markov chains, if the trace of Green matrix is finite, then the expectation of first leap time is uniformly bounded, both of which are proved to be equivalent for single birth processes. For birth–death processes, the explicit formulas are presented. As an application, we give the bounds of exponential convergence rates of (sub-) Markov semigroup Ptfrom l∞to l∞.