Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of...

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce...