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 disc rete times ti = i Delta for i = 1,..., N. We compare two non parametri c estimators of theta(t) which is assumed to be a piecewise constant f unction: wavelet estimator in the Haar basis and centred moving averag e estimator (CMAE), mean integrated square error (MISE) is proved to b e most often smaller for CMAE. Numerical simulation is done to illustr ate this fact. (C) Academie des Sciences/Elsevier, Paris