Research output: Contribution to journal › Article › peer-review
On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails. / Tesemnikov, Pavel Igorevich.
In: Сибирские электронные математические известия, Vol. 16, 2019, p. 1785-1794.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails
AU - Tesemnikov, Pavel Igorevich
N1 - Conference code: 57
PY - 2019
Y1 - 2019
N2 - 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”).
AB - 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”).
KW - convolution equivalence
KW - convolution tail
KW - heavy-tailed distributions
KW - random sums of random variables
KW - subexponential istributions
KW - the principle of a single big jump
UR - http://www.scopus.com/inward/record.url?scp=85097217790&partnerID=8YFLogxK
UR - https://www.elibrary.ru/item.asp?id=39545793
U2 - 10.33048/semi.2019.16.126
DO - 10.33048/semi.2019.16.126
M3 - Article
AN - SCOPUS:85097217790
VL - 16
SP - 1785
EP - 1794
JO - Сибирские электронные математические известия
JF - Сибирские электронные математические известия
SN - 1813-3304
T2 - Международная научная студенческая конференция (МНСК), Новосибирск, 14-19 апреля 2019
Y2 - 14 April 2019 through 19 April 2019
ER -
ID: 26206725