Colloquium - Alexander Sakhanenko
Institution: Sobolev Institute of Mathematics, Russia
Title: Non-classical boundary crossing problems for general random walks
Date: September 4, 2018
Location: C405 Wells Hall
Time: 10:20 AM - 11:10 AM
In this talk we consider non-classical random walks and investigate asymptotic behavior of the first-passage times over moving boundaries.
First, we consider random walks with independent but not necessarily identically distributed increments. Assuming only that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behavior of the first-passage times over moving boundaries.
Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to the time n, converges, as n tends to infinity, towards the Brownian meander.
Earlier such (non-logarithmic) asymptotic results were known only in the i.i.d. case for constant boundaries when the Wiener-Hopf factorization exists.
The talk is based on several works joint with Denis Denisov (University of Manchester, UK) and Vitali Wachtel (University of Augsburg, Germany).