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

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

215_1996_bearb.pdf - Published

Download (562kB)

URN: urn:nbn:de:bsz:180-madoc-17049
Document Type: Working paper
Year of publication: 1996
The title of a journal, publication series: None
Place of publication: Mannheim
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): 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.
Additional information:

Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.

Metadata export


+ Search Authors in

+ Download Statistics

Downloads per month over past year

View more statistics

You have found an error? Please let us know about your desired correction here: E-Mail

Actions (login required)

Show item Show item