Geodesic
On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1785-1794

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

We deal with two independent random walks with subexponential distributions of their increments. We study the tail distributional asymptotics for the sum of their partial maxima within random time intervals. Assuming the distributions of the lengths of these intervals to be relatively small, with respect to that of the increments of the random walks, we show that the sum of the maxima takes a large value mostly due a large value of a single summand (this is the so-called "principle of a single big jump").
Keywords: random sums of random variables, heavy-tailed distributions, subexponential istributions, the principle of a single big jump.
Mots-clés : convolution tail, convolution equivalence 
@article{SEMR_2019_16_a46,
     author = {P. I. Tesemnikov},
     title = {On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1785--1794},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a46/}
}
TY  - JOUR
AU  - P. I. Tesemnikov
TI  - On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1785
EP  - 1794
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a46/
LA  - ru
ID  - SEMR_2019_16_a46
ER  - 
%0 Journal Article
%A P. I. Tesemnikov
%T On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1785-1794
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a46/
%G ru
%F SEMR_2019_16_a46
P. I. Tesemnikov. On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1785-1794. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a46/