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Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II. The general case

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Abstract

In this paper we consider aperiodic ergodic Markov chains with transition probabilities exponentially small in a large parameter β. We extend to the general, not necessarily reversible case the analysis, started in part I of this work, of the first exit problem from a general domainQ containing many stable equilibria (attracting equilibrium points for the β=∞ dynamics). In particular we describe the tube of typical trajectories during the first excursion outsideQ.

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Olivieri, E., Scoppola, E. Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II. The general case. J Stat Phys 84, 987–1041 (1996). https://doi.org/10.1007/BF02174126

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Key Words

  • Markov chains
  • first exit problem
  • large deviations