Among the different generalizations of the CLT available on the web, I found these

- CLT for the sum of non-identical (and independent) random variables
- CLT for the sum of identical (and independent) multivariate random variables.

However, I can't find any for the sum of non-identical (and independent) multivariate variables.

Is it because it is straightforward ? Would the final covariance matrix be simply the sum of the individual ones ?

Thanks