Difference between cross correlation definitions (signal processing / random processes) I'm trying to understand the similarities/differences between the following definitions for cross correlation)
Signal Processing: (or it's discrete equivalent)
$$R_{XY}(\tau) = \int_{-\infty}^{+\infty} x^*(t) y(t+ \tau) dt$$
Random Processeses$$R_{XY}(t_1, t_2) = E\begin{Bmatrix}
X_{t_1} Y^*_{t_2}
\end{Bmatrix}$$
Are these related?
If the process is stationary it is ergodic, then time averages are equal to probabilistic averages.