论文标题
降雨过程模型与点过程的收敛
Convergence of Rain Process Models to Point Processes
论文作者
论文摘要
带有动力学的水分过程，在达到阈值后切换会导致降雨过程。这种降雨过程的特征是其干燥和潮湿时期的随机保留时间。平均而言，潮湿时期的保持时间比干燥的时间短得多。这里显示了降雨秋季过程到尖峰火车的积分过程的融合。点过程的基础水分过程是具有传送边界条件的阈值模型。这种近似允许使用许多精确公式来简化模型。收敛性通过Fokker-Planck推导，均方相对于连续功能，水分过程和均值相对于广义函数的均值收敛而显示的均方体收敛。
A moisture process with dynamics that switch after hitting a threshold gives rise to a rainfall process. This rainfall process is characterized by its random holding times for dry and wet periods. On average, the holding times for the wet periods are much shorter than the dry. Here convergence is shown for the rain fall process to a point process that is a spike train. The underlying moisture process for the point process is a threshold model with a teleporting boundary condition. This approximation allows simplification of the model with many exact formulas for statistics. The convergence is shown by a Fokker-Planck derivation, convergence in mean-square with respect to continuous functions, of the moisture process, and convergence in mean-square with respect to generalized functions, of the rain process.
