I have gone through some material that state that if two distributions are Gaussiand and are independent, then they are jointly Gaussian.
I was wondering if the same applies to Gaussian processes (GP). So if I have a GP $f_1 \sim GP(0,K_{11})$ and a GP $f_2 \sim GP(0,K_{22})$, then are both of them jointly Gaussian, even though their covariance functions are totally different and they might be evaluated over a different input range?.
Thank you