Reactive trajectories and the transition path process

• 成果类型: Article
• 署名作者: Lu, Jianfeng; Nolen, James
• 署名单位: Duke University; Duke University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0547-y
• 发表日期: 2015
• 页码: 195-244
• 关键词: reversible diffusion-processes; differential-equations; metastability; asymptotics; BOUNDARY; spdes

摘要

We study the trajectories of a solution to an It stochastic differential equation in , as the process passes between two disjoint open sets, and . These segments of the trajectory are called transition paths or reactive trajectories, and they are of interest in the study of chemical reactions and thermally activated processes. In that context, the sets and represent reactant and product states. Our main results describe the probability law of these transition paths in terms of a transition path process , which is a strong solution to an auxiliary SDE having a singular drift term. We also show that statistics of the transition path process may be recovered by empirical sampling of the original process . As an application of these ideas, we prove various representation formulas for statistics of the transition paths. We also identify the density and current of transition paths. Our results fit into the framework of the transition path theory by Weinan and Vanden-Eijnden.