论文标题
估计随机动力学系统最可能的过渡时间
Estimating the Most Probable Transition Time for Stochastic Dynamical Systems
论文作者
论文摘要
这项工作致力于研究随机动力学系统亚稳态状态之间最可能的过渡时间。这样的系统是由具有非散布布朗噪声的随机微分方程建模的，并在具有吸收边界的域中受到限制。我们没有最大程度地减少Onsager-Machlup动作功能，而是研究系统的解决方案过程留在过渡路径的邻域（或管）中，以表征最可能的过渡路径。我们首先建立指数衰减的下限和功率定律衰减上限，以最大程度地提高此概率。基于这些估计，我们在适当的条件下进一步得出了最可能的过渡时间和上限。最后，我们在简单的随机动力系统中说明了结果，并强调了与某些相关作品的关系。
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.
