I am working on the following problem in a course using "Stochastic Differential Equations" by Oksendal.
Consider the Ito SDE.
$dX_t=−λX_tdt+σdB_t$
Now state the variance spectrum of $\{X_t\}$ and argue that in the low frequency limit, the process can be considered white noise.
I know that this is an example of a Ornstein-Uhlenbeck process and that it can be solved analytically. Should I solve for the process, then find the autocovariance (can I assume stationarity?), then take the Fourier transform? Or there some method to go directly from the SDE?
Thanks for looking!