Tail asymptotics for the supremum of a random walk when the mean is not finite

D. Denisov, S. Foss, D. Korshunov

We consider the sums $S_n={\xi }_1+\cdots +{\xi }_n$ of independent identically distributed random variables. We do not assume that the $\xi$'s have a finite mean. Under subexponential type con…