随机扩散模型一种新的密度函数统计方法

引入核函数法对随机扩散方程（SDE）样本的密度分布进行统计，希望用核函数来减少统计涨落。由于SDE样本的密度随时间发展，越来越稀疏，所以核函数也应该越来越大，也就是说核函数应该随时间在变化。通过一个瞬时释放的二维扩散问题（具有解析解），从定性和定量两个角度比较了变带宽核函数法和传统统计方法在密度分布统计中的性能差别，论述了变带宽核函数法的优缺点，变带宽核函数法在牺牲部分峰值的前提下可以很好地解决SDE样本密度分布统计涨落问题，在工程应用中值得推广。

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.