# Compact embeddings for spaces of forward rate curves

## TL;DR

This paper proves a compact embedding result for spaces of forward rate curves, enabling approximation of forward rate evolutions by finite-dimensional processes.

## Contribution

It introduces a new compact embedding theorem for forward rate curve spaces, facilitating finite-dimensional approximations of their evolutions.

## Key findings

- Established a compact embedding theorem for forward rate curve spaces.
- Showed that forward rate evolutions can be approximated by finite-dimensional processes.
- Provided theoretical foundation for practical modeling of forward rate dynamics.

## Abstract

The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.