Max-Sum local equivalence of random variables with Farlie-Gumbel-Morgenstern joint distribution
Hui XU, Tao Jiang · Scientia Sinica Mathematica · 2016
In this paper, we study the local asymptotics for the sum and maximum of random variables with a certain Farlie-Gumbel-Morgenstern joint distribution, respectively. Then, under a suitable condition for local subexponentiality, we further obtain the local max-sum equivalence, which describes the big-jump principle of random walks from the local and dependent point of view.