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

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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
The title of a journal, publication series:	None
Publication language:	English
Institution:	School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
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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