Stability of solutions of parabolic PDEs with random drift and viscosity limit


Deck, Thomas ; Potthoff, Jürgen ; Våge, Gjermund ; Watanabe, Hisao


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URL: https://ub-madoc.bib.uni-mannheim.de/1704
URN: urn:nbn:de:bsz:180-madoc-17049
Document Type: Working paper
Year of publication: 1996
Place of publication: Mannheim
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
Subject headings (SWD): Stochastische partielle Differentialgleichung , Weißes Rauschen , Cauchy-Anfangswertproblem , Itô-Integralgleichung
Abstract: Let U a be the solution of the rtö stochastic parabolic Cauchy problem Du/&t - Lau = ~ . \7u, ult=o = f. We prove that U a depends continuously on a, when the coefficients in La converge to those in L o . This result is used to study the diffusion limit for the Cauchy problem (in Stratonovich sense): when the coefficients of La tends to 0 the corresponding solutions U a converge to a function Uo satisfying Duo/at = ~ 0 \7uo, ult=o = f. A criterion is provided for the existence of strong limits, e.g. U a ---+ Uo, in the space of Hida distributions (S)*. As an application we show that weak solutions of the above Cauchy problem are strong solutions.
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Deck, Thomas ; Potthoff, Jürgen ; Våge, Gjermund ; Watanabe, Hisao (1996) Stability of solutions of parabolic PDEs with random drift and viscosity limit. Open Access Mannheim [Working paper]
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