White noise and simulation of ordinary Gaussian processes

Puig Bénédicte and Poirion Fabrice
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Puig Bénédicte: ONERA, BP72 92322 Chatillon, France
Poirion Fabrice: ONERA, BP72 92322 Chatillon, France

Monte Carlo Methods and Applications, 2004, vol. 10, issue 1, 69-89

Abstract: A generalized process , where E is a nuclear space, is a random variable family such that the map is linear and continuous. The Gaussian white noise process is a well-known example. It is characterized by a Gaussian measure on the dual space E′ of E. Ordinary Gaussian processes can be constructed from the white noise process using the duality relation: where is a family of functions in E. 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 fixing the appropriate nuclear space E and family .

Date: 2004
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DOI: 10.1515/156939604323091216

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