UNIFORM RECONSTRUCTION OF GAUSSIAN-PROCESSES

We consider a Gaussian process X with smoothness comparable to the Bro wnian motion. We analyze reconstructions of X which are based on obser vations at finitely many points. For each realization of X the error i s defined in a weighted supremum norm, the overall error of a reconstr uction is defined as the pth moment of this norm. We determine the rat e of the minimal errors and provide different reconstruction methods w hich perform asymptotically optimal. In particular, we show that linea r interpolation at the quantiles of a certain density is asymptoticall y optimal. (C) 1997 Elsevier Science B.V.