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A new construction of random Colombeau distributions

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  • Çapar, Ulug
  • Aktuglu, Hüseyin

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.

Suggested Citation

  • Çapar, Ulug & Aktuglu, Hüseyin, 2001. "A new construction of random Colombeau distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 291-299, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:3:p:291-299
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