摘要
The Onsager-Machlup(OM)functional is well known for characterizing the most probable transition path of a diffusion process with non-vanishing noise.However,it suffers from a notorious issue that the functional is unbounded below when the specified transition time T goes to infinity.This hinders the interpretation of the results obtained by minimizing the OM functional.We provide a new perspective on this issue.Under mild conditions,we show that although the infimum of the OM functional becomes unbounded when T goes to infinity,the sequence of minimizers does contain convergent subsequences on the space of curves.The graph limit of this minimizing subsequence is an extremal of the abbreviated action functional,which is related to the OM functional via the Maupertuis principle with an optimal energy.We further propose an energy-climbing geometric minimization algorithm(EGMA)which identifies the optimal energy and the graph limit of the transition path simultaneously.This algorithm is successfully applied to several typical examples in rare event studies.Some interesting comparisons with the Freidlin-Wentzell action functional are also made.
基金
supported by National Natural Science Foundation of China(Grant Nos.11421101,91530322 and 11825102)
supported by the Construct Program of the Key Discipline in Hunan Province
supported by Singapore Ministry of Education Academic Research Funds(Grant Nos.R-146-000-267-114 and R-146-000-232-112)
National Natural Science Foundation of China(Grant No.11871365)。
