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
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Anmerkungen
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Journal of theoretical probability. - 35, 3 (2022) , 2052-2067, ISSN: 1572-9230
- Ereignis
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Veröffentlichung
- (wo)
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Freiburg
- (wer)
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Universität
- (wann)
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2022
- Urheber
- DOI
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10.1007/s10959-021-01107-3
- URN
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urn:nbn:de:bsz:25-freidok-2263918
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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25.03.2025, 13:54 MEZ
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Beteiligte
- Criens, David
- Ritter, Moritz
- Universität
Entstanden
- 2022
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