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We present a framework for modelling the star-formation histories of galaxiesas a stochastic process. We define this stochastic process through a powerspectrum density with a functional form of a broken power-law. Star-formationhistories are correlated on short timescales, the strength of this correlationdescribed by a power-law slope, $\alpha$, and they decorrelate to resemblewhite noise over a timescale that is proportional to the timescale of the breakin the power spectrum density, $\tau_{\rm break}$. We use this framework toexplore the properties of the stochastic process that, we assume, gives rise tothe log-normal scatter about the relationship between star-formation rate andstellar mass, the so-called galaxy star-forming main sequence. Specifically, weshow how the measurements of the normalisation and width ($\sigma_{\rm MS}$) ofthe main sequence, measured in several passbands that probe differenttimescales, give a constraint on the parameters of the underlying powerspectrum density. We first derive these results analytically for a simplifiedcase where we model observations by averaging over the recent star-formationhistory. We then run numerical simulations to find results for more realisticobservational cases. As a proof of concept, we use observational estimates ofthe main sequence scatter at $z\sim0$ and $M_{\star}\approx10^{10}~M_{\odot}$measured in H$\alpha$, UV+IR and the u-band, and show that combination of thesepoint to $\tau_{\rm break}=178^{+104}_{-66}$ Myr, when assuming $\alpha=2$.This implies that star-formation histories of galaxies lose "memory" of theirprevious activity on a timescale of $\sim200$ Myr, highlighting the importanceof baryonic effects that act over the dynamical timescales of galaxies.

Stochastic modeling of star-formation histories I: the scatter of the star-forming main sequence