Difference between cross correlation definitions (signal processing / random processes)

Question

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?

Answer 1

If the process is stationary it is ergodic, then time averages are equal to probabilistic averages.