# The Yamada-Watanabe Theorem for mild solutions to stochastic partial differential equations

## TL;DR

This paper extends the Yamada-Watanabe Theorem to semilinear stochastic partial differential equations with path-dependent coefficients, using the method of the moving frame to connect to infinite-dimensional stochastic differential equations.

## Contribution

It introduces a novel approach to prove the Yamada-Watanabe Theorem for SPDEs with path-dependent coefficients via the method of the moving frame.

## Key findings

- Established the Yamada-Watanabe Theorem for a new class of SPDEs.
- Reduced the proof to known results in infinite-dimensional SDEs.
- Provided a framework for analyzing path-dependent SPDEs.

## Abstract

We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called "method of the moving frame" allows us to reduce the proof to the Yamada-Watanabe Theorem for stochastic differential equations in infinite dimensions.