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Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II: The general case. (English) Zbl 1081.60542

Summary: We consider aperiodic ergodic Markov chains with transition probabilities exponentially small in a large parameter \(\beta\). We extend to the general, not necessarily reversible case the analysis, started in part I of this work [ibid. 79, No. 3/4, 613–647 (1995; Zbl 1081.60538)], of the first exit problem from a general domain \(Q\) containing many stable equilibria (attracting equilibrium points for the \(\beta =\infty\) dynamics). In particular we describe the tube of typical trajectories during the first excursion outside \(Q\).

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J50 Boundary theory for Markov processes

Citations:

Zbl 1081.60538
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References:

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