Strengthening ergodicity to geometric ergodicity for markov chains
Strengthening ergodicity to geometric ergodicity for markov chains
复制标题
将马尔可夫链的遍历性强化为几何遍历性
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
R. Tweedie
中科院分区：
文献类型：
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作者：
F. Spieksma;R. Tweedie
在本文中，我们发现的条件下，遍历马尔可夫链也是几何遍历的：也就是说，收敛到其极限几何迅速。我们证明了如果链的增量分布在适当的意义下具有均匀的指数尾，则更强的几何遍历性成立，而如果链的平稳测度π具有适当的指数尾，则几何遍历性再次成立，但在进一步的辅助条件下。我们给出的例子表明，特别是，π可能有几何尾巴，但链不需要几何遍历。我们的结论与一些例子，从神经网络和网络理论所涵盖的结果，表明使用的结果时，有一个已知的福斯特-李雅普诺夫函数，也当击中时间的有限集仅仅是
In this paper we find conditions under which ergodic Markov chains are also geometrically ergodic: that is, converge to their limits geometrically quickly. We show that if the increment distributions of the chain have uniform exponential tails in an appropriate sense, then the stronger geometric ergodicity hold, whilst if the stationary measure π of the chain has suitably exponential tails then again geometric ergodicity holds but under further auxiliary conditions. We give examples to show that, in particular, π may have geometric tails but the chain need not be geometrically ergodic. We conclude with a number of examples from queueing and network theory covered by the results, indicating the use of the results when there is a known Foster-Lyapunov function and also when the hitting times of finite sets are merely