A new construction of random Colombeau distributions

Ulug Çapar and Hüseyin Aktuglu

Statistics & Probability Letters, 2001, vol. 54, issue 3, 291-299

Abstract: In this paper a generalized random process is modeled through the randomization of a bilinear form between the space 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.

Keywords: Random; Colombeau; distributions; -duality; Extension; of; probability; measures; in; generalized; duals; Non-linear; functions; of; the; white; noise (search for similar items in EconPapers)
Date: 2001
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