  We present evidence for stochastic star formation histories in low-mass (M* <
10^10 Msun) galaxies from observations within the Galaxy And Mass Assembly
(GAMA) survey. For ~73,000 galaxies between 0.05<z<0.32, we calculate star
formation rates (SFR) and specific star formation rates (SSFR = SFR/M*) from
spectroscopic Halpha measurements and apply dust corrections derived from
Balmer decrements. We find a dependence of SSFR on stellar mass, such that
SSFRs decrease with increasing stellar mass for star-forming galaxies, and for
the full sample, SSFRs decrease as a stronger function of stellar mass. We use
simple parametrizations of exponentially declining star formation histories to
investigate the dependence on stellar mass of the star formation timescale and
the formation redshift. We find that parametrizations previously fit to samples
of z~1 galaxies cannot recover the distributions of SSFRs and stellar masses
observed in the GAMA sample between 0.05<z<0.32. In particular, a large number
of low-mass (M* < 10^10 Msun) galaxies are observed to have much higher SSFRs
than can be explained by these simple models over the redshift range of
0.05<z<0.32, even when invoking mass-dependent staged evolution. For such a
large number of galaxies to maintain low stellar masses, yet harbour such high
SSFRs, requires the late onset of a weak underlying exponentially declining SFH
with stochastic bursts of star formation superimposed.
