 94230 E. Olivieri, E. Scoppola
 MARKOV CHAINS WITH EXPONENTIALLY SMALL TRANSITION PROBABILITIES:
FIRST EXIT PROBLEM FROM A GENERAL DOMAIN
I. THE REVERSIBLE CASE.
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Jul 14, 94

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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 $\beta$.\par
We extend previous results by Freidlin and Wentzell ( [FW] ) on the first
exit problem from a general domain $Q$. \par
In the present paper we analyze the case of {\it reversible} Markov chains.
The general case will be studied in a forthcoming paper.\par
We prove, in a purely probabilistic way and without using 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 {\it cycles } and,
by using the new concept of {\it temporal entropy}, we
obtain new results
leading to a complete description of
the typical tube of trajectories during the first excursion outside
$Q$.\par
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