deletions | additions       diff --git a/untitled.tex b/untitled.tex  index b353611..ab1f4cc 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
  $$d^{P}f(t) + \alpha_{P-1} d^{P-1}f(t) + ... + \alpha_{0} f(t) = \beta_{Q}d^{Q}w(t) + \beta_{Q-1} d^{Q-1}w(t) + ... + w(t)$$    Where $d$ represents a change in a variable between times $t$ and $t + dt$, $f$ represents the state of the system minus the mean, and $w \sim IID\ N(0, \sigma^{2})$ continuous-time white noise random process representing the driving noise in the system due to non-linear effects. In this case, it will represent temperature fluctuations due to magnetohydrodynamic instabilities in the accretion disk. In order for the process to be stationary, $p \lt <  q$. The most well known example is the case where $p=1$ and $q=0$ CAR(1) process also known in the astronomical community as a damped random walk (DRW).   We construct the auto-regressive polynomial as the characteristic polynomial of the auto-regressive side of the CARMA process.