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

被引：8

作者：

Baudel, Manon ^{[1
]}

Guyader, Arnaud ^{[1
,2
]}

Lelievre, Tony ^{[1
,3
]}

机构：

[1] Ecole Ponts, CERMICS, Champs Sur Marne, France

[2] Sorbonne Univ, LPSM, Paris, France

[3] INRIA Paris, Paris, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2023年 / 155卷

基金：

欧洲研究理事会;

关键词：

Source-sink process; Hill relation; Transition path process; Reactive trajectory; Quasi-stationary distribution; QUASI-STATIONARY DISTRIBUTIONS; APPROXIMATION; STABILITY;

D O I：

10.1016/j.spa.2022.10.014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.(c) 2022 Published by Elsevier B.V.

引用

页码：393 / 436

页数：44

共 52 条

[1] Mixing times for uniformly ergodic Markov chains [J].