Publications de l'Institut Mathematique 2006 Volume 80, Issue 94, Pages: 47-57
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Regularly varying probability densities

Bingham N.H., Goldie Charles M., Omey Edward

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given.