Invariance principles for generalized domains of semistable attraction

Let X , X 1 , X 2 , … be independent and identically distributed R d -valued random vectors and assume X belongs to the generalized domain of attraction of some operator semistable law without normal component. Then without changing its distribution, one can redefine the sequence on a new probability space such that the properly affine normalized partial sums converge in probability and consequently even in L p (for some p > 0 ) to the corresponding operator semistable Lévy motion.