The Annals of Probability

First-passage times for random walks with nonidentically distributed increments

Denis Denisov, Alexander Sakhanenko, and Vitali Wachtel

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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.

Article information

Source
Ann. Probab., Volume 46, Number 6 (2018), 3313-3350.

Dates
Received: October 2016
Revised: September 2017
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1537862435

Digital Object Identifier
doi:10.1214/17-AOP1248

Mathematical Reviews number (MathSciNet)
MR3857857

Zentralblatt MATH identifier
06975488

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60F17: Functional limit theorems; invariance principles

Keywords
Random walk Brownian motion first-passage time overshoot moving boundary

Citation

Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali. First-passage times for random walks with nonidentically distributed increments. Ann. Probab. 46 (2018), no. 6, 3313--3350. doi:10.1214/17-AOP1248. https://projecteuclid.org/euclid.aop/1537862435


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