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

Let { X , X n , n ≥ 1 } be a sequence of independent identically distributed random variables with E X = 0 and assume that E X 2 I ( | X | ≤ x ) is slowly varying as x → ∞ , i.e., X 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.