On a Calculable Skorokhod's Integral Based Projection Estimator of the Drift Function in Fractional SDE

Abstract

This paper deals with a Skorokhod's integral based projection type estimator ${\hat{b}}_m$ of the drift function $b_0$ computed from $N\in {\mathbb{N}}^{\ast }$ independent copies $X^1,\dots ,X^N$ of the solution $X$ of $d{X}_t=b_0(X_t)dt+\sigma d{B}_t$, where $B$ is a fractional Brownian motion of Hurst index $H\in (1/2,1)$. Skorokhod's integral based estimators cannot be calculated directly from $X^1,\dots ,X^N$, but in this paper an ${\mathbb{L}}^2$-error bound is established on a calculable approximation of ${\hat{b}}_m$.

arXiv comment15 pages

References in corpus (6)

• Statistical aspects of the fractional stochastic calculus
• Ergodic theory for SDEs with extrinsic memory
• Nonparametric Estimation in Fractional SDE
• Nonparametric inference for fractional diffusion
• Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application
• On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE