An efficient approach to obtaining the exit location distribution and the mean first passage time based on the GCM method

In this paper, according to the probability evolution analysis, we developed a new procedure based on the Generalized Cell Mapping method to get the exit location distribution and the mean first passage time of the weak noise excited system. With the Generalized Cell Mapping method, the original stochastic process is converted into a Markov chain. Moreover, the eigenvalue problem of the elliptic differential operator for the escape problem is simplified into an eigenvalue problem of the probability transition matrix. Thus, the exit location distribution and the mean first passage time of the system can be easily derived by solving the transition matrix's eigenvalues and eigenvectors. By applying to the Maier-Stein system, Kramers problem, and the Vibro-impact system, shows the Generalized Cell Mapping method could save us a lot of time and provide us much better results compared with the directed Monte Carlo simulation. (C) 2021 Published by Elsevier B.V.