We model the time variability of \sim 9,000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk .
Using 2.7 million photometric measurements collected over 10 years , we confirm the results of Kelly et al .
( 2009 ) and Kozłowski et al .
( 2010 ) that this model can explain quasar light curves at an impressive fidelity level ( 0.01-0.02 mag ) .
The damped random walk model provides a simple , fast [ O ( N ) for N data points ] , and powerful statistical description of quasar light curves by a characteristic time scale ( \tau ) and an asymptotic rms variability on long time scales ( SF _ { \infty } ) .
We searched for correlations between these two variability parameters and physical parameters such as luminosity and black hole mass , and rest-frame wavelength .
Our analysis shows SF _ { \infty } to increase with decreasing luminosity and rest-frame wavelength as observed previously , and without a correlation with redshift .
We find a correlation between SF _ { \infty } and black hole mass with a power law index of 0.18 \pm 0.03 , independent of the anti-correlation with luminosity .
We find that \tau increases with increasing wavelength with a power law index of 0.17 , remains nearly constant with redshift and luminosity , and increases with increasing black hole mass with power law index of 0.21 \pm 0.07 .
The amplitude of variability is anti-correlated with the Eddington ratio , which suggests a scenario where optical fluctuations are tied to variations in the accretion rate .
However , we find an additional dependence on luminosity and/or black hole mass that can not be explained by the trend with Eddington ratio .
The radio-loudest quasars have systematically larger variability amplitudes by about 30 % , when corrected for the other observed trends , while the distribution of their characteristic time scale is indistinguishable from that of the full sample .
We do not detect any statistically robust differences in the characteristic time scale and variability amplitude between the full sample and the small subsample of quasars detected by ROSAT .
Our results provide a simple quantitative framework for generating mock quasar light curves , such as currently used in LSST image simulations .