ISSN:
1572-9613
Keywords:
Markov chains
;
first exit problem
;
large deviations
;
reversibility
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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 β. We extend previous results by M. I. Freidlin and A. D. Wentzell (FW) on the first exit problem from a general domainQ. In the present paper we analyze the case ofreversible Markov chains. The general case will be studied in a forthcoming paper. We probe, in a purely probabilistic way and without using the FW graphical technique, some results on the first exit problem from a general domainQ containing many attractors. In particular we analyze the properties of special domains calledcycles and, by using the new concept oftemporal entropy, we obtain new results leading to a complete description of the typical tube of trajectories during the first excursion outsideQ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02184873
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