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

Abstract

This paper deals with a Skorokhod's integral based least squares type estimator ${\hat{\theta }}_N$ 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 $H\in (1/3,1)$. On the one hand, some convergence results are established on ${\hat{\theta }}_N$ when $H=1/2$. On the other hand, when $H\ne 1/2$, Skorokhod's integral based estimators as ${\hat{\theta }}_N$ cannot be computed from data, but in this paper some convergence results are established on a computable approximation of ${\hat{\theta }}_N$.

34 pages, 6 figures

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• Statistical aspects of the fractional stochastic calculus
• Nonparametric estimation for interacting particle systems : McKean-Vlasov models
• Nadaraya-Watson Estimator for I.I.D. Paths of Diffusion Processes
• Nonparametric Estimation for I.I.D. Paths of a Martingale Driven Model with Application to Non-Autonomous Financial Models
• Nonparametric Drift Estimation from Diffusions with Correlated Brownian Motions

Cited by in corpus (2)

• Nonparametric Estimation of the Transition Density Function for Diffusion Processes
• On a Calculable Skorokhod's Integral Based Projection Estimator of the Drift Function in Fractional SDE