Exit location distribution in the stochastic exit problem by the generalized cell mapping method

The exit location distribution (ELD) in the stochastic exit problem is studied by the generalized cell mapping (GCM) method. According to the global properties of the underlying noise-free system, a proper bounded region is chosen in state space and divided into small cells. The one-step transient probability matrix that governs the global transient short-time solutions of the stochastic system is computed with the consideration of the absorbing boundary condition in exit problem. Based on it, the probability distribution of exit location on domain boundary can be obtained by sufficient evolution of system response starting from the attractor. Two typical examples are given to illustrate the application of the proposed GCM method. It shows that the results obtained by the GCM method agree well with either the results from direct numerical integration or the theoretical predictions.