The exit path of a Markov chain with rare transitions
The exit path of a Markov chain with rare transitions
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具有罕见转变的马尔可夫链的退出路径
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
R. Cerf
中科院分区：
文献类型：
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作者：
O. Catoni;R. Cerf
我们研究退出路径从一般域后，最后一次访问的一组马尔可夫链与罕见的转变。我们证明了几个大偏差原则的法律的循环访问（循环路径），连续的鞍点通过循环路径上的循环跳转到循环（鞍路径）和连续的所有点通过（出口路径）。我们估计的过程中花费在每个周期的周期路径的时间，以及它如何分解成花费在每个点的退出路径的时间。我们描述了一个系统的方法来找到最有可能的鞍路径。我们应用这些结果的可逆情况下的大都会动态。我们在附录中给出了相应的非齐次情形下的大偏差估计，它们是Catoni（1992）和Trouve（1992，1996a）已发表的工作的推论。
We study the exit path from a general domain after the last visit to a set of a Markov chain with rare transitions. We prove several large deviation principles for the law of the succession of the cycles visited by the process (the cycle path), the succession of the saddle points gone through to jump from cycle to cycle on the cycle path (the saddle path) and the succession of all the points gone through (the exit path). We estimate the time the process spends in each cycle of the cycle path and how it decomposes into the time spent in each point of the exit path. We describe a systematic method to find the most likely saddle paths. We apply these results to the reversible case of the Metropolis dynamics. We give in appendix the corresponding large deviation estimates in the non homogeneous case, which are corollaries of already published works by Catoni (1992) and Trouve (1992, 1996a).