A new construction of random Colombeau distributions

Abstract

In this paper a generalized random process is modeled through the randomization of a bilinear form between the space L of test functions and the Colombeau generalized functions. This results in a theory akin to Gelfand-Vilankin's random Schwartz distributions. An extension theorem in Bochner-Badrikian style is proved under some continuity assumptions. An important application is a natural representation of nonlinear functionals of white noise. (C) 2001 Elsevier Science B.V. All rights reserved.