Rain process models and convergence to point processes

A moisture process with dynamics that switch after hitting a threshold gives rise to rainfall process. This is characterized by its random holding times for dry and wet periods. On average, the periods are much shorter than dry. Here convergence shown rain fall point spike train. The underlying model teleporting boundary condition. approximation allows simplification of many exact formulas statistics. Fokker-Planck derivation, in mean-square respect continuous functions, process, generalized