Geodesic
Sufficient conditions for the subexponential property of the convolution of two distributions
Matematičeskie zametki, Tome 58 (1995) no. 5, pp. 778-781.

Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions on the distributions of two independent nonnegative random variables $X$ and $Y$ are given for the sum $X+Y$ to have a subexponential distribution, i.e., $(1-F^{(2*)}(t))/(1-F(t))\to2$ as $t\to+\infty$, where $F(t)=\mathsf P\{X+Y\le t\}$ and $F^{(2*)}(t)$ is the convolution of $F(t)$ with itself. 
@article{MZM_1995_58_5_a11,
     author = {A. L. Yakymiv},
     title = {Sufficient conditions for the subexponential property of the convolution of two distributions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {778--781},
     publisher = {mathdoc},
     volume = {58},
     number = {5},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a11/}
}
TY  - JOUR
AU  - A. L. Yakymiv
TI  - Sufficient conditions for the subexponential property of the convolution of two distributions
JO  - Matematičeskie zametki
PY  - 1995
SP  - 778
EP  - 781
VL  - 58
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a11/
LA  - ru
ID  - MZM_1995_58_5_a11
ER  - 
%0 Journal Article
%A A. L. Yakymiv
%T Sufficient conditions for the subexponential property of the convolution of two distributions
%J Matematičeskie zametki
%D 1995
%P 778-781
%V 58
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a11/
%G ru
%F MZM_1995_58_5_a11
A. L. Yakymiv. Sufficient conditions for the subexponential property of the convolution of two distributions. Matematičeskie zametki, Tome 58 (1995) no. 5, pp. 778-781. http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a11/

[1] Chistyakov V. P., “Teorema o summakh nezavisimykh polozhitelnykh sluchainykh velichin i ee prilozhenie k vetvyaschimsya sluchainym protsessam”, Teor. ver. i ee primen., 9:4 (1964), 710–718 | MR | Zbl

[2] Sgibnev M. S., “Asimptotika bezgranichno delimykh raspredelenii v $R$”, Sib. matem. zh., 31:1 (1990), 135–140 | MR

[3] Chover J., Ney P., Wainger S., “Degeneracy properties of subcritical branching processes”, Ann. Prob., 1 (1973), 663–673 | DOI | MR | Zbl

[4] Teugels J. L., “The class of subexponential distributions”, Ann. Prob., 3 (1975), 1000–1011 | DOI | MR | Zbl

[5] Goldie C. M., “Subexponential distributions and dominated-variation tails”, J. Appl. Prob., 15 (1978), 440–442 | DOI | MR | Zbl

[6] Embrechts P., Goldie C. M., “On closure and factorisation properties of subexponential and related distributions”, J. Austral. Math. Soc., 29 (1980), 243–256 | DOI | MR | Zbl

[7] Cline D. B. H., “Convolution of distributions with exponential and subexponential tails”, J. Austral. Math. Soc., 43 (1987), 347–365 | DOI | MR | Zbl

[8] Kluppelberg C., “Subexponential distributions and integrated tails”, J. Appl. Prob., 25 (1988), 132–141 | DOI | MR

[9] Leslie J. R., “On the non-closure under convolution of the subexponential family”, J. Appl. Prob., 26 (1989), 58–66 | DOI | MR | Zbl

[10] Jakimiv A. L., “Limit theorems for random $A$-permutations”, Proc. 3-rd Petrozavodsk Conf. on Probab. Methods in Discr. Math., 1993, 459–469