# Affine realizations with affine state processes for stochastic partial differential equations

## TL;DR

This paper investigates conditions under which stochastic partial differential equations with affine realizations can be represented using affine state processes, providing characterizations and practical examples such as the HJMM equation.

## Contribution

It offers a characterization of initial points for affine realizations in SPDEs and illustrates the results with relevant examples from finance.

## Key findings

- Characterization of initial points for affine realizations
- Conditions for affine realizations in SPDEs
- Application to the HJMM equation in finance

## Abstract

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.