论文标题
Martingale估计贝塞尔过程的功能
Martingale estimation functions for Bessel processes
论文作者
论文摘要
在本文中，我们根据基于扩散算子的本征函数得出了BESSEL过程的维度参数的Martingale估计函数。由于贝塞尔过程是非恋爱的，并且针对千古扩散而开发了martingale估计函数的理论，因此我们使用贝塞尔过程的时空转换，并为修改的贝塞尔过程提出了结果。我们推断一致性，渐近态性并讨论最佳性。事实证明，基于修改后的贝塞尔过程的第一个本征功能的martingale估计函数与Cox Ingersoll Ross过程的线性Martingale估计函数一致。此外，我们的结果也可以应用于估计一维dunkl过程的多重性参数。
In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on the eigenfunctions of the diffusion operator. Since a Bessel process is non-ergodic and the theory of martingale estimating functions is developed for ergodic diffusions, we use the space-time transformation of the Bessel process and formulate our results for a modified Bessel process. We deduce consistency, asymptotic normality and discuss optimality. It turns out that the martingale estimating function based of the first eigenfunction of the modified Bessel process coincides with the linear martingale estimating function for the Cox Ingersoll Ross process. Furthermore, our results may also be applied to estimating the multiplicity parameter of a one-dimensional Dunkl process.
