mean value of a correlated variables product

I everybody,
I have a problem and I was thinking if somebody could help me;
I have to calculate the mean value

$E[y_{i}^{2} y_{j}^{2}]$

per $i \neq j$

where $y_{i}$ and $y_{j}$ are two samples of the same process y which is gaussian with 0 mean and known sqare value $\sigma_{y}^{2}$ .

The problem is that the correlation of the process is exponential:
$R_{y}[k] = \rho^{\vert k \vert} \sigma_{y}^{2}$ ;

I believe I should calculate the joint probability density function but I don't know how.
Please could somebody help me, or simply tell me a good reference where I can find this topic?

Thanks a lot.