  To gain insights into long-term Active Galactic Nuclei (AGN) variability, we
analyze an AGN sample from the Sloan Digital Sky Survey (SDSS) and compare
their photometry with observations from the Hyper Suprime-Cam survey (HSC)
observed $\langle 14.85 \rangle$ years after SDSS. On average, the AGN are
fainter in HSC than SDSS. We demonstrate that the difference is not due to
subtle differences in the SDSS versus HSC filters or photometry. The decrease
in mean brightness is redshift dependent, consistent with expectations for a
change that is a function of the rest-frame time separation between
observations. At a given redshift, the mean decrease in brightness is stronger
for more luminous AGN and for objects with longer time separation between
measurements. We demonstrate that the dependence on redshift and luminosity of
measured mean brightness decrease is consistent with simple models of Eddington
ratio variability in AGN on long (Myr, Gyr) timescales. We show how our results
can be used to constrain the variability and demographic properties of AGN
populations.
