Extreme values and the multivariate compact law of the iterated logarithm (Q5950025)

Consider iid random vectors \( X_1, X_2,\dots\) in \( R^d \). Assume \(X\) belongs to the generalized domain of attraction of the (multivariate) Gaussian law \(N\), i.e. there exist operators \(T_n\) and vectors \(b_n\) such that \( T_nS_n - b_n \Rightarrow N \) where \(S_n\) is the partial sum of \(X_k\). The author proves a LIL when finitely many maximal (in a certain sense) terms are omitted from the partial sum. Then the limiting cluster set is the closed unit ball if \(X\) satisfies an additional integrability condition that characterizes the number of the omitted extrema.