A non linear parabolic equation with noise : a reduction method

Benth, Fred Espen ; Gjessing, Håkon K.

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URL: http://ub-madoc.bib.uni-mannheim.de/1730
URN: urn:nbn:de:bsz:180-madoc-17304
Document Type: Working paper
Year of publication: 1994
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: 60H15 35R60 60G20 46F05 46F12 ,
Subject headings (SWD): Semilineare Differentialgleichung , Weißes Rauschen , Nichtlineare parabolische Differentialgleichung
Keywords (English): semilinear stochastic partial differential equations , white noise analysis , Wick product , splitting method
Abstract: In this paper we study a class of parabolic equations with a non-linear gradient term. The system is disturbed by white noise in time. We show that the solution of this problem can be represented as the Wick product between a normalized random variable of exponential form and the solution of a nonlinear parabolic equation. We allow random initial data which might be anticipating. A relation between the Wick product with a normalized exponential and translation is proved in order to establish our results.
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