Limit theorems for self-normalized large deviation

Let X, X-1, X-2,... be i.i.d. random variables with zero mean and fnite variance (sigma(2). It is well known that a fnite exponential moment assumption is necessary to study limit theorems for large deviation for the standardized partial sums. In this paper, limit theorems for large deviation for self-normalized sums are derived only under fnite moment conditions. In particular, we show that, if EX4 < infinity.