线性增长条件下扩散系数的非参数估计

摘要

本文研究了一维扩散方程中,当扩散系数为满足线性增长条件的Lipschitz函数,而不是有界Lipschitz函数时,扩散系数的非参数估计问题.利用鞅的性质,将扩散方程的估计问题纳入了非参数回归的框架.%In this paper, we study nonparametric estimation of the diffusion coefficientof 1-dimensional diffusion process, in which the diffusion coefficient is a linear growthLipschitz function other than a bounded Lipschitz function. Using the properties ofmartingale, we translate the problems in diffusion to nonparametric regression setting.