deletions | additions       diff --git a/CAR Generation.tex b/CAR Generation.tex  index 4b35f8a..81e17d9 100644  --- a/CAR Generation.tex  +++ b/CAR Generation.tex 
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\begin{equation}  M(t) = e^{-t/\tau} M(0) + \bar{M}(1-e^{-t/\tau}) + \sigma\int_{0}^{t} e^{-(t-s)/\tau} dB(s),  \end{equation}  where $M$ is the magnitude of an image, $\tau$ is a characteristic timescale in days, $\bar{M}$ is the mean magnitude of the light curve in the absence of fluctuations, and $\sigma$ is the characteristic amplitude of the fluctuations in mag/day$^{1/2}$. In this model, fluctuations are generated by the integral term where $dB(s)$ is a mean zero normally distributed value with width $dt$. By fitting the above model to the data, [REF] generated a distribution of $\tau$ and $\sigma$ for the MACHO quasars; we show typical examples of the CAR process with reasonable values for those parameters in Figure \ref{fig:example_lcs}. While the damped random walk process provides a good description of the data obtained so far, it is not yet clear whether it will remain a good description for longer baseline, higher cadence or multi-filter lightcurves. The different emission regions of an AGN -- different parts of the accretion disk, broad and narrow line clouds, and so on -- are likely to vary in different ways, suggesting that sums of stochastic processes could provide more accurate descriptions still (REF: Kelly); these subcomponents would likely need parameters drawn from different distributions to the one above, and the correlations between the processes may need to be taken into account as well. Nevertheless, the success of the CAR model with the data we have makes it a sensible place to begin when simulating LSST-like AGN light curves.