Asymptotics for sums of random variables with local subexponential behaviour

S. Asmussen, S. Foss, D. Korshunov

We study distributions $F$ on $[0,\infty )$ such that for some $T\le \infty$, $F^{\ast 2}(x,x+T]\sim 2F(x,x+T]$. The case $T=\infty$ corresponds to $F$ being subexponential, and our ana…