# First-passage times for random walks with nonidentically distributed increments

@article{Denisov2018FirstpassageTF, title={First-passage times for random walks with nonidentically distributed increments}, author={Denis Denisov and Alexander I. Sakhanenko and Vitali Wachtel}, journal={The Annals of Probability}, year={2018} }

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.

## 9 Citations

### First-passage time asymptotics over moving boundaries for random walk bridges

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The moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge, leading to a possible phase transition depending on the order of the distance between zero and the moving boundary.

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### First-Passage Times over Moving Boundaries for Asymptotically Stable Walks

- MathematicsTheory of Probability & Its Applications
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Let $\{S_n, n\geq1\}$ be a random walk wih independent and identically distributed increments and let $\{g_n,n\geq1\}$ be a sequence of real numbers. Let $T_g$ denote the first time when $S_n$ leaves…

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### First-Passage Times for Random Walks in the Triangular Array Setting

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In this paper we continue our study of exit times for random walks with independent but not necessarily identical distributed increments. Our paper "First-passage times for random walks with…

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