On metastability

Consider finite state space irreducible and absorbing Markov processes. A general spectral criterion is provided for the absorbing time to be close to an exponential random variable, whatever the starting point. When exiting points are added to the state space, our criterion also insures that the ex...

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Bibliographic Details
Published in:Probability theory and related fields 2022-10, Vol.184 (1-2), p.275-322
Main Author: Miclo, Laurent
Format: Article
Language:English
Subjects:
Algebra
Criteria
Economics
Economics and Finance
Eigenvalues
Finance
Humanities and Social Sciences
Insurance
Management
Markov analysis
Markov processes
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Metastable state
Operations Research/Decision Theory
Poisson equation
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random variables
Statistics for Business
Theoretical
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Description
Summary:Consider finite state space irreducible and absorbing Markov processes. A general spectral criterion is provided for the absorbing time to be close to an exponential random variable, whatever the starting point. When exiting points are added to the state space, our criterion also insures that the exit time and position are almost independent. Since this is valid for any exiting extension of the state space, it corresponds to an instance of the metastability phenomenon. Simple examples at small temperature suggest that this new spectral criterion is quite sharp. But the main interest of the underlying quantitative approach, based on Poisson equations, is that it does not rely on a small parameter such as temperature, nor on reversibility.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-022-01147-8