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On the Hill relation and the mean reaction time for metastable processes

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  • Baudel, Manon
  • Guyader, Arnaud
  • Lelièvre, Tony

Abstract

We illustrate how the Hill relation and the notion of quasi-stationary distribution can be used to analyse the biasing error introduced by many numerical procedures that have been proposed in the literature, in particular in molecular dynamics, to compute mean reaction times between metastable states for Markov processes. The theoretical findings are illustrated on various examples demonstrating the sharpness of the biasing error analysis as well as the applicability of our study to elliptic diffusions.

Suggested Citation

  • Baudel, Manon & Guyader, Arnaud & Lelièvre, Tony, 2023. "On the Hill relation and the mean reaction time for metastable processes," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 393-436.
    • Handle: RePEc:eee:spapps:v:155:y:2023:i:c:p:393-436
    DOI: 10.1016/j.spa.2022.10.014
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    References listed on IDEAS

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    1. Aldous, David & Lovász, László & Winkler, Peter, 1997. "Mixing times for uniformly ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 165-185, November.
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