Estimating the most probable transition time for stochastic dynamical systems

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