随机动力系统最可能转移时间的估计
Estimating the Most Probable Transition Time for Stochastic Dynamical Systems
摘要：
本文研究随机动力系统在亚稳态之间的最可几跃迁时间。这种系统由一个带有非零布朗噪声的随机微分方程来描述，并被限制在一个具有吸收边界的区域内。为了刻画最可能的转移路径，我们不求Onsager-Machlup作用泛函的最小值，而是研究系统的解过程停留在转移路径邻域（或管道）内的最大概率，首先建立该概率最大值的指数衰减下界和幂律衰减上界.基于这些估计，我们进一步推导出最可能的过渡时间的上下界，在适当的条件下。最后，我们在简单的随机动力系统中说明了我们的结果，并强调了与一些相关工作的关系。
英文摘要：
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and is restricted in a domain with absorbing boundary. Instead of minimizing the Onsager-Machlup action functional, we examine the maximum probability that the solution process of the system stays in a neighborhood (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.
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