mean value of a correlated variables product

May 2010
1
0
I everybody,
I have a problem and I was thinking if somebody could help me;
I have to calculate the mean value

\(\displaystyle E[y_{i}^{2} y_{j}^{2}] \)

per \(\displaystyle i \neq j\)

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

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

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.