A new construction of random Colombeau distributions

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• 作者：Ç ; apar ; Ulug ; Aktuglu ; Hü ; seyin
• 关键词：28C20 ; 46F99 ; 60B05 ; 60G20 ; Random Colombeau distributions ; C¯ ; -duality ; Extension of probability measures in generalized duals ; Non-linear functions of the white noise
• 刊名：Statistics and Probability Letters
• 出版年：2001
• 出版时间：October 1, 2001
• 年：2001
• 卷：54
• 期：3
• 页码：291-299
• 全文大小：136 K

文摘

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