Bingham, N. H.; Goldie, Charles M.; Omey, Edward Regularly varying probability densities. (English) Zbl 1164.26302 Publ. Inst. Math., Nouv. Sér. 80(94), 47-57 (2006). The authors prove that the convolution of regularly varying probability densities is asymptotically equivalent to their sum. Various extensions of this result are given, concerning densities with tails which are rapidly varying, O-regularly varying, almost decreasing, of bounded decrease. Cases involving subexponentiality remain open. Reviewer: Slobodanka Janković (Beograd) Cited in 6 Documents MSC: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 60E05 Probability distributions: general theory Keywords:almost decreasing; convolution of densities; O-regular variation; rapid variation; regular variation PDFBibTeX XMLCite \textit{N. H. Bingham} et al., Publ. Inst. Math., Nouv. Sér. 80(94), 47--57 (2006; Zbl 1164.26302) Full Text: DOI EuDML