Some results about the large deviations principle in white noise analysis

Timpel, Matthias

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URN: urn:nbn:de:bsz:180-madoc-17004
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 , Große Abweichung
Abstract: In recent years, there has been an enormous interest in the theory of large deviations, i.e. in the asymptotic behaviour of small probabilities on an exponential scale. Although the roots of this theory can be dated back to Cramér in 1938 it took until the mid-1970's that starting with Donsker and Varadhan the subject exploded. Numbers of publications have been written since then, and the subject has found many applications to related fields like statistical mechanics or others. On the other hand white noise analysis provides lots of powerful tools as well for irrfinitedimensional calculus as for probability theory, a quite complete overview is given by. So the combination of these two subjects should inspire new results and give a feed-back to each of them. In the present paper I will do a very first step towards this aim stating some large deviations results in the context of white noise analysis. Not only the white noise probability measure μ will be considered, but also a certain dass of functionals over the white noise space (S' (IR), Β, μ) turns out to correspond to measures as first shown independently. For some of these measures large deviations results can be shown as well.
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