Convergence of the all-time supremum of a Lévy process in the heavy-traffic regime

Kamil Marcin Kosinski, Onno Boxma, Bert Zwart

In this paper we derive a technique of obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each $a>0$, let $\{Y_n^{(a)}:n\ge 1\}$ be a s…