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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

   
 
 

 

The dual Yamada–Watanabe theorem for mild solutions to stochastic partial differential equations


Author: S. Tappe
Journal: Theor. Probability and Math. Statist. 105 (2021), 51-68
MSC (2020): Primary 60H15; Secondary 60H10, 60H05
DOI: https://doi.org/10.1090/tpms/1155
Published electronically: December 7, 2021
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Abstract: We provide the dual result of the Yamada–Watanabe theorem for mild solutions to semilinear stochastic partial differential equations with path-dependent coefficients. An essential tool is the so-called “method of the moving frame”, which allows us to reduce the proof to infinite dimensional stochastic differential equations.


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Additional Information

S. Tappe
Affiliation: Department of Mathematical Stochastics, Albert Ludwig University of Freiburg, Ernst-Zermelo-Straße 1, D-79104 Freiburg, Germany
Email: stefan.tappe@math.uni-freiburg.de

Keywords: Stochastic partial differential equation, martingale solution, mild solution, dual Yamada–Watanabe theorem, uniqueness in law, joint uniqueness in law, pathwise uniqueness
Received by editor(s): May 18, 2021
Published electronically: December 7, 2021
Additional Notes: The author gratefully acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 444121509
Article copyright: © Copyright 2021 Taras Shevchenko National University of Kyiv