Modul: MAT971 Stochastische Prozesse

## First-passage times over moving boundaries for random walks with non-identically distributed increments

Prof. Dr. Vitali Wachtel talk

Speaker invited by: Prof. Dr. Erwin Bolthausen

**Date:** 26.02.20 **Time:** 17.15 - 19.00 **Room:** Y27H12

We consider a random walk $S_n$ with independent but not necessarily identical distributed increments. Assuming that increments satisfy the Lindeberg condition, we investigate the tail behaviour of the stopping time $T_g=\min\{n:x+S_n\leq g_n\}$ for a large class of boundaries $\{g_n\}$. We also prove limit theorems for $S_n$ conditioned on$\{T_g>n\}$. At the end of the talk we shall also consider the situation when the Lindeberg condition is not fulfilled, but the central limit theorem is still valid.