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

TL;DR

This paper extends the Yamada-Watanabe theorem to mild solutions of semilinear stochastic PDEs with path-dependent coefficients, using the method of the moving frame to facilitate the proof.

Contribution

It introduces a dual version of the Yamada-Watanabe theorem for stochastic PDEs with path-dependent coefficients, employing the method of the moving frame.

Findings

Established the dual Yamada-Watanabe theorem for mild solutions

Reduced the proof to infinite dimensional SDEs using the moving frame method

Provided a framework for analyzing path-dependent stochastic PDEs

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.