Extreme values and a Gaussian central limit theorem (Q1071368)

We examine the central limit theorem with Gaussian limit law for a sequence of independent, identically distributed, vector valued random variables whose partial sums can be centered and normalized to be tight with non-degenerate limit laws. These results apply to the situation when the sequence is in the domain of attraction of a non-degenerate stable law of index \(p\in (0,2]\), and are achieved by eliminating the extreme values from the partial sums.