TL;DR
This paper reviews recent advances in understanding the metastable behavior of continuous-time Markov chains, focusing on their characterization via martingale problems to analyze their long-term dynamics.
Contribution
It provides a comprehensive review of recent results on metastability in Markov chains using martingale problem characterizations, highlighting new theoretical insights.
Findings
Characterization of metastability through martingale problems
Recent theoretical results on metastable Markov chains
Framework for analyzing long-term behavior of Markov processes
Abstract
We review recent results on the metastable behavior of continuous-time Markov chains derived through the characterization of Markov chains as unique solutions of martingale problems.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Stochastic processes and statistical mechanics · Stochastic processes and financial applications