On a calculable Skorokhod’s integral based projection estimator of the drift function in fractional SDE

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