On the orthogonal representation of generalized random fields

Abstract

An orthogonal representation for a class of generalized random fields defined on an infinite-dimensional separable Hilbert space is studied. This representation is an extension of the expansion studied in Ruiz-Medina and Angulo (1995). The results are applied to obtain the orthogonal expansion for a linear functional of a zero-mean, second-order random field satisfying certain regularity conditions. Finally, some applications of the above representation in obtaining linear prediction estimates, and in obtaining explicit-form solutions to stochastic partial differential equations, are discussed.