On a theorem by A.S. Cherny for semilinear stochastic partial differential equations
Abstract: We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by a cylindrical Brownian motion. The solutions are allowed to take values in Banach spaces. We show that weak uniqueness is equivalent to weak joint uniqueness, and thereby generalize a theorem by A.S. Cherny to an infinite dimensional setting. Our proof for the technical key step is different from Cherny’s and uses cylindrical martingale problems. As an application, we deduce a dual version of the Yamada–Watanabe theorem, i.e. we show that strong existence and weak uniqueness imply weak existence and strong uniqueness
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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Journal of theoretical probability. - 35, 3 (2022) , 2052-2067, ISSN: 1572-9230
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2022
- Creator
- DOI
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10.1007/s10959-021-01107-3
- URN
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urn:nbn:de:bsz:25-freidok-2263918
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:54 PM CET
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Criens, David
- Ritter, Moritz
- Universität
Time of origin
- 2022