Estimate Exponential Large Mean Exit Time for Diffusion Process

We propose an efficient numerical method to estimate the mean exit time of a high dimensional diffusion process associated with an Ito SDE with a gradient drift and small $\epsilon$ diffusion coefficient, starting from a stable equilibrium of the drift. It is well-known that the mean exit time is exponential large in $\epsilon$ and thus the direct simulation of the SDE requires long time integration. Our method only requires the simulation time $O(1 / \epsilon)$ and is based on the Ornstein-Uhlenbeck diffusion in each dimension.