Theory of Probability and Mathematical Statistics
The dual Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations
S. Tappe
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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.
Keywords: Stochastic partial differential equation, martingale solution, mild solution, dual Yamada–Watanabe theorem, uniqueness in law, joint uniqueness in law, pathwise uniqueness
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