On the maximum of a perturbed random walk

27.01.2020, 12:15  –  Campus Golm Haus 9 Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Andrey Pilipenko (Kyiv)

Abstract. Let \((\xi_1,\eta_1), (\xi_2,\eta_2),\ldots\) be asequence of i.i.d. two-dimensional random vectors. We prove a functional limit theorem for the maximum of a perturbed random walk \(\underset{0\leq k\leq n}{\max}\,(\xi_1+\ldots+\xi_k+\eta_{k+1})\) in a situation where its asymptotics is affected by both \(\underset{0\leq k\leq n}{\max}\,(\xi_1+\ldots+\xi_k)\) and \(\underset{1\leq k\leq n}{\max}\,\eta_k\) to a comparable extent. The talk is based on the joint work with A.Iksanov and I.Samoilenko.