漂移向量与扩散矩阵的非参数估计模型

考虑多维扩散过程的非参数估计问题.利用It扩散的性质,将漂移向量和扩散矩阵的样本表示成带有测量误差的回归模型,并讨论了系统误差的L~r上界以及随机误差项的收敛速度,建立了漂移向量与扩散矩阵非参数估计的通用模型.

Nonparametric Estimation Model of the Drift Vector and the Diffusion Matrix

The nonparametric estimation problem for multi-dimensional diffusion processes is considered.Using the properties of Ito diffusion,the samples of drift vector and diffusion matrix are represented by the regression model with measurement error.The L~r upper bound of the stochastic error and the L~r convergence rate of the measurement error are given.The generic models for nonparametric estimation of the drift vector and diffusion matrix are established.