Abstract
Suppose X and Y are independent nonnegative random variables. We study the behavior of P( XY> t), as t → ∞, when X has a subexponential distribution. Particular attention is given to obtaining sufficient conditions on P( Y> t) for XY to have a subexponential distribution. The relationship between P( X> t) and P( XY> t) is further studied for the special cases where the former satisfies one of the extensions of regular variation.
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