A Review of White Noise Analysis from a Probabilistic Standpoint

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URL:	https://ub-madoc.bib.uni-mannheim.de/1703
URN:	urn:nbn:de:bsz:180-madoc-17034
Document Type:	Working paper
Year of publication:	1996
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
Subject headings (SWD):	Weißes Rauschen , Transformation <Mathematik> , Messbarkeit , Martingal
Abstract:	The main notions and tools from white noise analysis are set up on the basis of the calculus of Gaussian random variables and the S-transform. A new proof of the formula for the S-transform of Itô integrals is given. Moreover, measurability and the martingale property with respect to the Brownian filtration are characterized in terms of the S-transform. This allows to extend these notions to random variables and processes, respectively, in the space of Hida distributions.
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