Abstract

In this paper, we propose a non parametric functional estimator for diffusion coefficient in integrated stochastic diffusion process. The asymptotic bias of the kernel type estimator and the new proposed non parametric estimator for diffusion coefficient are developed when the time span is fixed, and we can see that the new non parametric estimator has a smaller asymptotic bias than the kernel estimator. Moreover, the consistency and the asymptotic normality of the new proposed non parametric estimator are explored under some mild conditions.

中文翻译：

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集成扩散过程中扩散系数的非参数偏差降低

摘要

在本文中，我们提出了一种集成随机扩散过程中扩散系数的非参数泛函估计器。在时间跨度固定的情况下，开发了核类型估计器的渐近偏差和新提出的扩散系数非参数估计器，我们可以看到新的非参数估计器比核估计器具有更小的渐近偏差。此外，在一些温和条件下探索了新提出的非参数估计器的一致性和渐近正态性。