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
Deutsche Nationalbibliothek Frankfurt am Main
Extent
Online-Ressource
Language
Englisch
Notes
Journal of theoretical probability. - 35, 3 (2022) , 2052-2067, ISSN: 1572-9230

Event
Veröffentlichung
(where)
Freiburg
(who)
Universität
(when)
2022
Creator

DOI
10.1007/s10959-021-01107-3
URN
urn:nbn:de:bsz:25-freidok-2263918
Rights
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Last update
25.03.2025, 1:54 PM CET

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Time of origin

  • 2022

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