Multi-scale metastable dynamics and the asymptotic stationary distribution of perturbed Markov chains

DOI10.1016/j.spa.2016.05.003zbMath1348.60107arXiv1412.6979OpenAlexW2388048240MaRDI QIDQ326849

Stéphane Le Roux, Volker Betz

Publication date: 12 October 2016

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.6979

zbMATH Keywords

algorithmasymptoticsescape timeslimiting stationary distributionnon-reversible Markov chains

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Numerical analysis or methods applied to Markov chains (65C40)

Related Items (5)

CONVERGENCE OF GIBBS MEASURES OF A PERTURBED SYSTEM OF GRAPH ITERATED FUNCTIONS WITH DEGENERATION ⋮ Metastable distributions of Markov chains with rare transitions ⋮ Perturbed finite-state Markov systems with holes and Perron complements of Ruelle operators ⋮ Spectral Theory for Random Poincaré Maps ⋮ Perturbations of parabolic equations and diffusion processes with degeneration: boundary problems, metastability, and homogenization

Cites Work

• Unnamed Item
• Computing the asymptotic spectrum for networks representing energy landscapes using the minimum spanning tree
• Flows in complex networks: theory, algorithms, and application to lennard-Jones cluster rearrangement
• Markov chains with exponentially small transition probabilities: first exit problem from a general domain. I: The reversible case.
• Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II: The general case.
• Metastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit times
• Metastability in reversible diffusion processes. II: Precise asymptotics for small eigenvalues
• Metastability and low lying spectra in reversible Markov chains
• Tunneling and metastability of continuous time Markov chains. II: The nonreversible case
• From random Poincaré maps to stochastic mixed-mode-oscillation patterns
• A Dirichlet principle for non reversible Markov chains and some recurrence theorems
• A combinatorial approach to nearly uncoupled Markov chains. I: Reversible Markov chains
• Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems
• Fast multilevel methods for Markov chains
• Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution
• Noise-Induced Phenomena in Slow-Fast Dynamical Systems
• The Evolution of Conventions
• Parallelizing the Computation of PageRank
• Aggregation of Variables in Dynamic Systems
• Geometric bounds on iterative approximations for nearly completely decomposable Markov chains
• Brownian motion in a field of force and the diffusion model of chemical reactions
• Metastability

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