Strassen-type law of the iterated logarithm for self-normalized increments of sums

Let {X,Xn,n≥1}{X,Xn,n≥1} be a sequence of independent identically distributed random variables with EX=0EX=0 and assume that EX2I(|X|≤x)EX2I(|X|≤x) is slowly varying as x→∞x→∞, i.e., XX is in the domain of attraction of the normal law. In this paper it is shown that a Strassen-type functional law of the iterated logarithm holds for self-normalized increments of sums of such random variables.