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.
Keywords
- White Noise
- Wiener Process
- Topological Vector Space
- Parameter Domain
- Stochastic Partial Differential Equation
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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
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