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where $\{Z_t\}$ is a white noise process with zero mean and variance $\sigma^2$. For any autocovariance function $\gamma(h)$ for which $\lim_{h\to\infty}\gamma(h) = 0$ and any integer $k > 0$, there exists an ARMA(p,q) process with autocovariance function $\gamma_X(h)$ such that $\gamma_X(h) = \gamma(h)$ for all $h \leq k$. These relations make the ARMA process a very useful tool in the analysis and modeling of many different time-series.   %(reword this blurb, too much directly from the text)   In reality, the underlying phenomena driving AGN variability are not discrete processes. In order to get a proper understanding of the underlying physics and structure of the AGN, we need a continuous analog to the ARMA process.  %\!\!BE SURE TO CITE BROCKWELL AND DAVIS TIME SERIES THEORY AND METHODS  %**Quick intro to ARMA (an maybe a bit of stochastic analysis) 
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%**ARMA is discrete, mention why we need a continuous method instead  \subsection{CARMA}  In reality, the underlying phenomena driving AGN variability are not discrete processes. In order to get a proper understanding of the underlying physics and structure of the AGN, we need a continuous analog to the ARMA process.  A continuous-time ARMA (CARMA) process is the continuous case of the discrete ARMA process. A system described by a CARMA process obeys the stochastic differential equation     $$d^{P}f(t) + \alpha_{P-1} d^{P-1}f(t) + ... + \alpha_{0} f(t) = \beta_{Q}d^{Q}w(t) + \beta_{Q-1} d^{Q-1}w(t) + ... + w(t)$$