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 -