A statistical method for the density function of the stochastic differential model function

In this paper, the density distribution of stochastic diffusion equation (SDE) is calculated by the kernel function method, and the statistical fluctuation is reduced by the kernel function. As the density of SDE over time is sparser and sparser, the kernel function is bigger and bigger, i.e., the kernel function is changing over time, and the rule is given by a method called the variable bandwidth kernel function method. Through an instantaneous release of a two-dimensional diffusion problem (with the analytical solution), from the perspective of both qualitative and quantitative comparisons of the variable bandwidth kernel function method and the traditional statistical method in the performance of density distribution statistical difference, this paper discusses the advantages and disadvantages of variable bandwidth kernel function method. The variable bandwidth kernel function method which sacrifices part of the peak can be very good to solve the problem of SDE density distribution statistical fluctuation, and it is worth promoting in engineering applications.