On the distribution tail of the sum of the maxima of two randomly stopped sums in the presence of heavy tails

摘要

We deal with two independent random walks with subexponentialdistributions of their increments. We study the tail distributionalasymptotics for the sum of their partial maxima within random timeintervals. Assuming the distributions of the lengths of these intervals tobe relatively small, with respect to that of the increments of the randomwalks, we show that the sum of the maxima takes a large value mostlydue a large value of a single summand (this is the so-called "principle ofa single big jump").