  Inspired by applications, we consider reaction-diffusion equations on
$\mathbb{R}$ that are stochastically forced by a small multiplicative noise
term that is white in time, coloured in space and invariant under translations.
We show how these equations can be understood as a stochastic partial
differential equation (SPDE) forced by a cylindrical Q-Wiener process and
subsequently explain how to study stochastic travelling waves in this setting.
In particular, we generalize the phase tracking framework that was developed in
[Hamster & Hupkes 2017] and [Hamster & Hupkes 2018] for noise processes driven
by a single Brownian motion. The main focus lies on explaining how this
framework naturally leads to long term approximations for the stochastic wave
profile and speed. We illustrate our approach by two fully worked-out examples,
which highlight the predictive power of our expansions.
