Correlation in weak stationary process I read this chapter about weakly stationary process from the book "Introduction to Probability, Statistics, and Random Processes" by Hossein Pishro-Nik.
Here is the defition of it:
$$E[X(t_1)]=E[X(t_2)]$$
$$E[X(t_1)X(t_2)]=E[X(t_1+\Delta)X(t_2+\Delta)]  = R_X(t_1,t_2)$$
The first equation is about equality of means and the second one is about equality of correlation function.
Then author writes that

The second condition states that the correlation function $R_X(t_1,t_2)$ is only a function of $\tau=t_1−t_2$, and not $t_1$ and $t_2$ individually.

I have a question about it.
How from $E[X(t_1+\Delta)X(t_2+\Delta)]$ follows that correlation depends only from $t_2 - t_1$?

The equation holds for any $\Delta$.  So you can set $\Delta= -t_1$.  You would get $E[X(t_1) X(t_2)] = E[X(t_1 + \Delta) X(t_2 + \Delta)] = E[X(0) X(t_2-t_1)]$.  The last expression depends only on $t_2-t_1$.
