On the representation of weakly continuous stochastic processes

• A novel approach to obtaining series representations in the stochastic mean for weakly, and therefore mean square, continuous stochastic processes 1s presented. Two distinct orthogonal series representations are derived for the entire class of weakly continuous stochastic processes on any Lebesgue set of the real line, and a constructive procedure to obtain them explicitly is given. They include as particular cases all earlier representations. Also they are shown to converge almost surely in the norm of an L2 space. Two general results, on which the development of this paper is based, are also presented. The maj or part of this work was done while the author was at the Electrical Engineering Department, Princeton University. His work was supported in part by the National Science Foundation under Grant GK-1439 with Princeton University and by the National Science Foundation under Grant GU-2059 with the University of North Carolina at Chapel Hill. ** This author's work was supported by the National Science Foundation under Grant GK-13l92.