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

01/13/2023

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by   Nicolas Marie, et al.

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This paper deals with a Skorokhod's integral based least squares type estimator θ_N of the drift parameter θ_0 computed from N∈ℕ^* copies X^1,…,X^N of the solution X to dX_t =θ_0b(X_t)dt +σ dB_t, where B is a fractional Brownian motion of Hurst index H∈ [1/2,1). On the one hand, a risk bound is established on θ_N when H = 1/2 and X^1,…,X^N are dependent copies of X. On the other hand, when H > 1/2, Skorokhod's integral based estimators as θ_N cannot be computed directly from data, but in this paper some convergence results are established on a computable approximation of θ_N when X^1,…,X^N are independent.