A construction of processes with one dimensional martingale marginals, based upon path-space Ornstein-Uhlenbeck processes and the Brownian sheet

Abstract

Using a variation from the construction of the Ornstein-Uhlenbeck process on canonical path-space C ([0 , 1]; R ) in terms of the Brownian sheet, we obtain a large class of processes, adapted to the Brownian filtration, which admit the one dimensional marginals of a martingale.