MARKOV CHAINS WITH EXPONENTIALLY SMALL TRANSITIONPROBABILITIES : FIRST EXIT PROBLEM FROM A GENERAL DOMAINI
MARKOV CHAINS WITH EXPONENTIALLY SMALL TRANSITIONPROBABILITIES : FIRST EXIT PROBLEM FROM A GENERAL DOMAINI
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具有指数小转移概率的马尔可夫链:一般域的首次退出问题
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
E. Scoppola
中科院分区：
文献类型：
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作者：
E. Olivieri;E. Scoppola
我们考虑具有有限状态空间的一般遍历非周期马尔可夫链，其不同通信状态对之间的转移概率在大参数下呈指数小。我们扩展了 Freidlin 和 Wentzell (FW]) 先前关于一般域 Q 的第一个退出问题的结果。在本文中，我们分析了可逆马尔可夫链的情况。一般情况将在即将发表的论文中进行研究。我们以纯粹概率的方式并且不使用 F-W 图形技术证明了来自包含许多吸引子的一般域 Q 的第一个退出问题的一些结果。特别是，我们分析了称为循环的特殊域的属性，并通过使用时间熵的新概念，我们获得了新的结果，从而完整地描述了 Q 之外的第一次偏移期间的典型轨迹管。
We consider general ergodic aperiodic Markov chains with nite state space whose transition probabilities between pairs of diierent communicating states are exponentially small in a large parameter. We extend previous results by Freidlin and Wentzell (FW]) on the rst exit problem from a general domain Q. In the present paper we analyze the case of reversible Markov chains. The general case will be studied in a forthcoming paper. We prove, in a purely probabilistic way and without using F-W graphical technique, some results on the rst exit problem from a general domain Q containing many attractors. In particular we analyze the properties of special domains called cycles and, by using the new concept of temporal entropy, we obtain new results leading to a complete description of the typical tube of trajectories during the rst excursion outside Q.