Subexponentiality of the product of independent random variables
D. B. H. Cline and
Stochastic Processes and their Applications, 1994, vol. 49, issue 1, 75-98
Suppose X and Y are independent nonnegative random variables. We study the behavior of P(XY>t), as t --> [infinity], 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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