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November 2018 First-passage times for random walks with nonidentically distributed increments
Denis Denisov, Alexander Sakhanenko, Vitali Wachtel
Ann. Probab. 46(6): 3313-3350 (November 2018). DOI: 10.1214/17-AOP1248

Abstract

We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time $n$ converges, as $n\to\infty$, towards the Brownian meander.

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Denis Denisov. Alexander Sakhanenko. Vitali Wachtel. "First-passage times for random walks with nonidentically distributed increments." Ann. Probab. 46 (6) 3313 - 3350, November 2018. https://doi.org/10.1214/17-AOP1248

Information

Received: 1 October 2016; Revised: 1 September 2017; Published: November 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06975488
MathSciNet: MR3857857
Digital Object Identifier: 10.1214/17-AOP1248

Subjects:
Primary: 60G50
Secondary: 60F17, 60G40

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 6 • November 2018
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