First-passage times for random walks with non-identically distributed increments

Denis Denisov; Alexander Sakhanenko; Vitali Wachtel

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arXiv · 1611.00493

First-passage times for random walks with non-identically distributed increments

Denis Denisov·Alexander Sakhanenko·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.

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Denis Denisov, Alexander Sakhanenko, Vitali Wachtel. 2016-11-02. First-passage times for random walks with non-identically distributed increments. https://arxiv.org/abs/1611.00493

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