| 陈萍,冯予.漂移向量与扩散矩阵的非参数估计模型[J].数学年刊A辑,2011,32(4):497~506 |
| 漂移向量与扩散矩阵的非参数估计模型 |
| Nonparametric Estimation Model of the Drift Vector and the Diffusion Matrix |
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| DOI： |
| 中文关键词: 漂移向量 扩散矩阵 非参数回归 通用模型 |
| 英文关键词:Drift vector Diffusion matrix Nonparametric regression Generic models |
| 基金项目:国家社会科学基金(No09BTJ004)资助的项目 |
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| 中文摘要: |
| 考虑多维扩散过程的非参数估计问题. 利用It\^{o}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. |
| 英文摘要: |
| The nonparametric estimation problem for multi-dimensional diffusion processes is considered.
Using the properties of It\^{o} 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. |
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