White noise and simulation of ordinary Gaussian processes

s — A generalized process (XÁ; ¿ 2 E), where E is a nuclear space, is a random variable family such that the map ¿ 7! XÁ is linear and continuous. The Gaussian white noise process is a wellknown example. It is characterized by a Gaussian measure on the dual space E 0 ofE . Ordinary Gaussian processes can be constructed from the white noise process using the duality relation: (X Á = h_;¿ xi; x 2 Rd)where ( ¿ x; x 2 Rd) is a family of functions inE . The goal of this paper is to show that all the classical simulation methods of Gaussian processes found in the literature are derived from this construction, by Ž xing the appropriate nuclear space E and family ( ¿ x; x 2 R).