- 95-423 Enzo Olivieri, Elisabetta Scoppola
- MARKOV CHAINS WITH EXPONENTIALLY SMALL TRANSITION
FIRST EXIT PROBLEM FROM A GENERAL DOMAIN
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Sep 14, 95
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Abstract. In this paper we consider aperiodic ergodic Markov chains with transition
probabilities exponentially small in a large parameter $\b$ .
We extend to the general not necessarily reversible case
the analysis started in [OS]
of the first exit problem from a general domain $Q$ containing many stable
equilibria (attracting equilibrium points for the $\b = \infty$ dynamics).
In particular we describe the tube of typical trajectories during the first
excursion outside $Q$.