Power and exponential moments of the number of visits and related quantities for perturbed random walks

Gerold Alsmeyer, Alexander Iksanov, Matthias Meiners

Let $({\xi }_1,{\eta }_1),({\xi }_2,{\eta }_2),...$ be a sequence of i.i.d.\ copies of a random vector $(\xi ,\eta )$ taking values in ${\mathbb{R}}^2$, and let $S_n:={\xi }_1+...+{\xi }_n$. The sequence $(S_{n-1} + η_n)_{n \ge…