论文标题
I.I.D.的非参数估计分数SDE的路径
Nonparametric Estimation for I.I.D. Paths of Fractional SDE
论文作者
论文摘要
本文介绍了从独立连续观测计算出的漂移函数的非参数估计量，按紧凑的时间间隔计算出的，该解决方案的解决方案是由分数布朗尼运动（FSDE）驱动的随机微分方程。首先，在Skorokhod的基于不可分割的最小二乘甲骨文$ \ widehat b $ $ b $上建立了风险约束。由于FSDE解决方案与其初始条件的衍生物之间的关系，因此在可计算的$ \ widehat b $的可计算近似值中推断出风险界限。另一个限制是直接建立在$ b'$的估计器中进行比较的。在紧凑的三角学基础上或$ \ mathbb r $ $ supported hermite的基础上，这些估计量的一致性和收敛速度是为这些估计值建立的。
This paper deals with nonparametric estimators of the drift function $b$ computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion (fSDE). First, a risk bound is established on a Skorokhod's integral based least squares oracle $\widehat b$ of $b$. Thanks to the relationship between the solution of the fSDE and its derivative with respect to the initial condition, a risk bound is deduced on a calculable approximation of $\widehat b$. Another bound is directly established on an estimator of $b'$ for comparison. The consistency and rates of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the $\mathbb R$-supported Hermite basis.
