Mean integrated square error for different estimators of the diffusion coefficient of a diffusion process

Let (X-t) be a diffusion process satisfying X-t = b(t, X-t)dt + theta(t)h(X-t)dW(t), a sample path of this process (X-t) is observed at discrete times ti = i Delta for i = 1,..., N. We compare two non parametric estimators of theta(t) which is assumed to be a piecewise constant function: wavelet estimator in the Haar basis and centred moving average estimator (CMAE), mean integrated square error (MISE) is proved to be most often smaller for CMAE. Numerical simulation is done to illustrate this fact. (C) Academie des Sciences/Elsevier, Paris