  Accreting compact objects show variations in source flux over a broad range
of timescales and in all wavebands. The light curves typically show a lognormal
distribution of flux and a linear relation between flux and rms. It has been
demonstrated that an exponential transform of an underlying (and unobserved)
Gaussian stochastic process provides a very good description of the light
curves with these observed properties. Recently, a non-stationary power
spectrum was observed on fast timescales (~ days) in the active galaxy, IRAS
13224--3809, as well as a non-lognormal flux distribution and non-linear
rms-flux relation. Here, we investigate the affects of piecewise non-stationary
power spectra on the resultant flux distribution and rms-flux relation. We
demonstrate that the simple "exponentiation" model successfully reproduces the
observed quantities, even when the light curves are non-stationary. We also
demonstrate how non-lognormal flux distributions and rms-flux relations
inconsistent with a linear model can be erroneously produced from poorly
sampled PSDs. This is of particular importance for AGN surveys where very long
baselines are required to sample the PSD down to low enough frequencies.
