  The amount of power contained in the variations in galaxy star-formation
histories (SFHs) across a range of timescales encodes key information about the
physical processes which modulate star formation. Modelling the SFHs of
galaxies as stochastic processes allows the relative importance of different
timescales to be quantified via the power spectral density (PSD). In this
paper, we build upon the PSD framework and develop a physically-motivated,
"stochastic" prior for non-parametric SFHs in the spectral energy distribution
(SED)-modelling code Prospector. We test this prior in two different regimes:
1) massive, $z = 0.7$ galaxies with both photometry and spectra, analogous to
those observed with the LEGA-C survey, and 2) $z = 8$ galaxies with photometry
only, analogous to those observed with NIRCam on JWST. We find that it is able
to recover key galaxy parameters (e.g. stellar mass, stellar metallicity) to
the same level of fidelity as the commonly-used continuity prior. Furthermore,
the realistic variability information incorporated by the stochastic SFH model
allows it to fit the SFHs of galaxies more accurately and precisely than
traditional non-parametric models. In fact, the stochastic prior is $\gtrsim
2\times$ more accurate than the continuity prior in measuring the recent
star-formation rates (log SFR$_{100}$ and log SFR$_{10}$) of both the $z = 0.7$
and $z = 8$ mock systems. While the PSD parameters of individual galaxies are
difficult to constrain, the stochastic prior implementation presented in this
work allows for the development hierarchical models in the future, i.e.
simultaneous SED-modelling of an ensemble of galaxies to measure their
underlying PSD.
