On a Dual Pair of Spaces of Smooth and Generalized Random Variables

Potthoff, Jürgen ; Timpel, Matthias

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URL: https://ub-madoc.bib.uni-mannheim.de/1725
URN: urn:nbn:de:bsz:180-madoc-17259
Document Type: Working paper
Year of publication: 1993
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 60H30 60H07 60H05 46E50 46A13 46F25 ,
Subject headings (SWD): Weißes Rauschen , Zufallsvariable , Ornstein-Uhlenbeck-Operator
Keywords (English): white noise analysis , smooth and generalized random variables , white noise probability space , exonentials of the Ornstein-Uhlenbeck operator
Abstract: A dual pair G and G* of smooth and generalized random variables, respectively, over the white noise probability space is studied. G is constructed by norms involving exponentials of the Ornstein-Uhlenbeck operator, G* is its dual. Sufficient criteria are proved for when a function on S(IR) is the S-transform of an element in G or G*.
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