this is for holding javascript data
Jack O'Brien edited untitled.tex
almost 8 years ago
Commit id: 084c1b285960ec743e4c2dd87114e8ee14a1d7ab
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index c45c1c0..4c752c5 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 $w \sim
IID\ N(0, WN(0, \sigma^{2})$ 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, $p < q$. 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.