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
Data provider
This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the 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
Other Objects (12)
Parameter estimation for semilinear stochastic partial differential equations
Foundations of the theory of semilinear stochastic partial differential equations
Some numerical techniques for approximating semilinear parabolic (stochastic) partial differential equations
Linear and semilinear partial differential equations : an introduction
Semilinear and quasilinear stochastic evolution equations in Banach spaces
The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations
Stochastic Partial Differential Equations: An Introduction
Limit theorems and statistical inference for solutions of some stochastic (partial) differential equations
Segmentation of Stochastic Images using Stochastic Partial Differential Equations
Level-2 large deviations and semilinear stochastic equations for symmetric diffusions
Numerical approximation methods for semilinear partial differential equations with gradient-dependent nonlinearities
Stochastic partial differential equations and surface growth
Parameter estimation for semilinear stochastic partial differential equations
Foundations of the theory of semilinear stochastic partial differential equations
Some numerical techniques for approximating semilinear parabolic (stochastic) partial differential equations
Linear and semilinear partial differential equations : an introduction
Semilinear and quasilinear stochastic evolution equations in Banach spaces
The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations
Stochastic Partial Differential Equations: An Introduction
Limit theorems and statistical inference for solutions of some stochastic (partial) differential equations
Segmentation of Stochastic Images using Stochastic Partial Differential Equations
Level-2 large deviations and semilinear stochastic equations for symmetric diffusions
Numerical approximation methods for semilinear partial differential equations with gradient-dependent nonlinearities
Stochastic partial differential equations and surface growth
Parameter estimation for semilinear stochastic partial differential equations
Foundations of the theory of semilinear stochastic partial differential equations
Some numerical techniques for approximating semilinear parabolic (stochastic) partial differential equations
Linear and semilinear partial differential equations : an introduction
Semilinear and quasilinear stochastic evolution equations in Banach spaces
The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations
Stochastic Partial Differential Equations: An Introduction
Limit theorems and statistical inference for solutions of some stochastic (partial) differential equations
Segmentation of Stochastic Images using Stochastic Partial Differential Equations
Level-2 large deviations and semilinear stochastic equations for symmetric diffusions
Numerical approximation methods for semilinear partial differential equations with gradient-dependent nonlinearities