Estimating the most probable transition time for stochastic dynamical systems. (21st June 2021)

• Record Type: Journal Article
• Authors: Huang, Yuanfei; Chao, Ying; Wei, Wei; Duan, Jinqiao
• Is Part Of: Nonlinearity. Volume 34:Number 7(2021)
• Page Start: 4543
• Page End: 4569
• Publication Date: 2021-06-21
• Subjects: stochastic differential equations -- most probable transition time -- Onsager–Machlup action functional -- metastable states -- rare events; 60H10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abf33d
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems with non-vanishing Brownian noise. Instead of minimizing the Onsager–Machlup action functional, we examine the maximum probability that the solution process of the system stays in a neighbourhood (or a tube) of a transition path, in order to characterize the most probable transition path. We first establish the exponential decay lower bound and a power law decay upper bound for the maximum of this probability. Based on these estimates, we further derive the lower and upper bounds for the most probable transition time, under suitable conditions. Finally, we illustrate our results in simple stochastic dynamical systems, and highlight the relation with some relevant works.