On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE

This paper deals with a Skorokhod’s integral based least squares type estimator ${\widehat{\theta }}_N$ of the drift parameter ${\theta }_0$ computed from $N\in {\mathbb{N}}^{\ast }$ (possibly dependent) copies $X^1,\dots ,X^N$ of the solution $X$ of $d{X}_t={\theta }_{0}b(X_t)dt+\sigma d{B}_t$, where $B$ is a fractional Brownian motion of Hurst index $H\in (1\mathrm{/}3,1)$. On the one hand, some convergence results are established on ${\widehat{\theta }}_N$ when $H=1\mathrm{/}2$. On the other hand, when $H\mathrm{\ne }1\mathrm{/}2$, Skorokhod’s integral based estimators as ${\widehat{\theta }}_N$ cannot be computed from data, but in this paper some convergence results are established on a computable approximation of ${\widehat{\theta }}_N$.