Functional limit theorems for the maxima of perturbed random walks and divergent perpetuities in the $M_1$-topology

Alexander Iksanov, Andrey Pilipenko, Igor Samoilenko

Let $({\xi }_1,{\eta }_1)$, $({\xi }_2,{\eta }_2),\dots$ be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the $J_1$-topolo…