# 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.

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