Phase transitions and metastability in Markovian and molecular systems
type: Item
instance of: scholarly article
title: Phase transitions and metastability in Markovian and molecular systems
zbMATH Open document ID: 1041.60026
author: Wilhelm Huisinga
author: Christof Schütte
author: Sean P. Meyn
published in: The Annals of Applied Probability
publication date: 2004-06-10T00:00:00Z
review text: The purpose of this paper is to develop foundations for model reduction and new modeling techniques for diffusion models. These foundations are all based upon the recent spectral theory of Markov process. The main assumption imposed is V-uniform ergodicity of the process. Under this assumption the authors show that the associated semigroup admits a spectral gap in a weighted \(L_{\infty}\)-norm and real eigenfunctions provide a decomposition of the state space into ``almost''-absorbing subsets. The authors also show that the process mixes rapidly in each of these subsets prior to existing and that the conditional distributions of exit times are approximately exponential. These results represent a significant expansion of the classical Wentzell-Freidlin theory.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 2072704
zbMATH Keywords: large deviations
zbMATH Keywords: Markov process
reviewed by: Zdzisław Rychlik
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1075828057
OpenAlex ID: W2025335914
cites work: Multiplicative ergodicity and large deviations for an irreducible Markov chain.
cites work: Laplace approximations for large deviations of nonreversible Markov processes. The nondegenerate case
cites work: Metastability in stochastic dynamics of disordered mean-field models
cites work: Metastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit times
cites work: Metastability and low lying spectra in reversible Markov chains
cites work: Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymp\-totics.
cites work: Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains
cites work: Asymptotic evaluation of certain markov process expectations for large time. IV
cites work: Exponential and uniform ergodicity of Markov processes
cites work: Q3409967
cites work: Exit probabilities and optimal stochastic control
cites work: Asymptotic series and exit time probabilities
cites work: Risk-Sensitive Control on an Infinite Time Horizon
cites work: Asymptotic for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential
cites work: Q3672830
cites work: Two-sided taboo limits for Markov processes and associated perfect simulation.
cites work: Structural characterization of taboo-stationarity for general processes in two-sided time.
cites work: A note on asymptotic expansions for Markov chains using operator theory
cites work: Large deviations asymptotics and the spectral theory of multiplicatively regular Markov proces\-ses
cites work: Spectral theory and limit theorems for geometrically ergodic Markov processes
cites work: Q4197143
cites work: Q3995203
cites work: Spectral Analysis of Fokker--Planck and Related Operators Arising From Linear Stochastic Differential Equations
cites work: Contrôlabilité des Systèmes non Linéaires
cites work: Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
cites work: Q4273571
cites work: Markov chains and stochastic stability
cites work: Stability of Markovian processes II: continuous-time processes and sampled chains
cites work: General Irreducible Markov Chains and Non-Negative Operators
cites work: Asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators
cites work: Fluctuations of the entropy production in anharmonic chains
cites work: A direct approach to conformational dynamics based on hybrid Monte Carlo
cites work: Q4524854
cites work: Q4544264
cites work: On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states
cites work: Q5670045
cites work: Controllability of nonlinear systems
cites work: Q4943608
cites work: Quasi-stationary distributions for Markov chains on a general state space
cites work: Q3341599
DOI: 10.1214/AOAP/1075828057
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description: scientific article; zbMATH DE number 2072704