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White noise in space and time as the time-derivative of a cylindrical Wiener process

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Stochastic Partial Differential Equations and Applications II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1390))

Abstract

The concept of white noise in space and time N arising in the context of stochastic partial differential equations is related to Wiener processes with values in Hilbert spaces of distributions w. (or a cylindrical Wiener process).

It is shown, that w. induces a distribution-valued random variable W on the same parameter domain as N. N and W are connected by the relation =N.

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References

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Author information

Authors and Affiliations

  1. Institut für dynamische Systeme, Universität Bremen, West Germany

    Kay-Uwe Schaumlöffel

Authors
  1. Kay-Uwe Schaumlöffel
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Giuseppe Da Prato Luciano Tubaro

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© 1989 Springer-Verlag

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Schaumlöffel, KU. (1989). White noise in space and time as the time-derivative of a cylindrical Wiener process. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083950

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  • DOI: https://doi.org/10.1007/BFb0083950

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51510-4

  • Online ISBN: 978-3-540-48200-0

  • eBook Packages: Springer Book Archive

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