# Foundations of the theory of semilinear stochastic partial differential equations

## TL;DR

This review article surveys the fundamental concepts and results related to semilinear stochastic partial differential equations, focusing on solution types, their interrelations, and existence and uniqueness theorems.

## Contribution

It provides a comprehensive overview of the foundational theory of semilinear stochastic PDEs, including detailed explanations of solution concepts and a standard existence and uniqueness proof.

## Key findings

- Clarification of strong, weak, and mild solutions
- Connections between different solution concepts
- Standard existence and uniqueness results established

## Abstract

The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish their connections, and review a standard existence- and uniqueness result. The proof of the existence result is based on a slightly extended version of the Banach fixed point theorem.