2016/01/01 by Giacomo Di Gesù, Tony Lelièvre, Dorian Le Peutrec +1 · 42 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Gene Regulatory Network Analysis #Jump #Jump process #Markov Chains and Monte Carlo Methods #Markov chain #Markov kernel #Markov model #Markov process #Markov property #Markov renewal process #State space #math-ph #math.AP #math.MP #math.PR #msc:35P20 #msc:60J60 #physics.chem-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1039/c6fd00120c
published in Faraday Discussions 195, 469-495 (Royal Society of Chemistry) · 14 pages
openalex publication_date 2016/01/01 · arxiv created 2016/05/09 · openalex created_date 2016/06/24 · arxiv updated 2017/02/08 · openalex updated_date 2026/08/05
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the notion of quasi-stationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the Eyring-Kramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.