随机扩散模型一种新的密度函数统计方法

发布时间：2018-06-17 06:28

  本文选题：随机扩散方程 + 扩散输运方程　； 参考：《强激光与粒子束》2017年12期

【摘要】：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。
[Abstract]:The kernel function method is introduced to calculate the density distribution of the random diffusion equation (SDE) samples, and it is hoped that the kernel function can be used to reduce the statistical fluctuation. Because the density of SDE samples is more and more sparse with time, so the kernel function should be bigger and larger, that is to say, the kernel function should change with time. Through a two-dimensional diffusion problem with instantaneous release (with analytical solution), the performance differences between the variable bandwidth kernel function method and the traditional statistical method in density distribution statistics are compared qualitatively and quantitatively. The advantages and disadvantages of the variable bandwidth kernel function method are discussed. The variable bandwidth kernel function method can solve the statistical fluctuation problem of SDE sample density distribution at the premise of sacrificing partial peak value, and it is worth popularizing in engineering application.
【作者单位】： 杭州电子科技大学信息工程学院;
【基金】：国家自然科学基金项目(11475050,61503109,11705041) 浙江省科技厅公益性项目(2015C33035)
【分类号】：O211.63
，

本文编号：2030071