MARKOV-CHAINS WITH EXPONENTIALLY SMALL TRANSITION-PROBABILITIES - FIRST EXIT PROBLEM FROM A GENERAL DOMAIN .1. THE REVERSIBLE CASE

被引:64
作者
OLIVIERI, E [1 ]
SCOPPOLA, E [1 ]
机构
[1] UNIV BARI,DIPARTMENTO FIS,I-70126 BARI,ITALY
关键词
MARKOV CHAINS; FIRST EXIT PROBLEM; LARGE DEVIATIONS; REVERSIBILITY;
D O I
10.1007/BF02184873
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider general ergodic aperiodic Markov chains with finite state space whose transition probabilities between pairs of different communicating states are exponentially small in a large parameter beta. We extend previous results by M. I. Freidlin and A. D. Wentzell (FW) on the first 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 the FW graphical technique, some results on the first 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 first excursion outside Q.
引用
收藏
页码:613 / 647
页数:35
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