Local asymptotics for the area under the random walk excursion

Elena Perfilev; Vitali Wachtel

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arXiv · 1708.06189

Local asymptotics for the area under the random walk excursion

Elena Perfilev·Vitali Wachtel

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Abstract

We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and light-tailed increments. We determine the asymptotics for local probabilities for the area and prove a local central limit theorem for the duration of the excursion conditioned on the large values of its area.

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Elena Perfilev, Vitali Wachtel. 2017-08-21. Local asymptotics for the area under the random walk excursion. https://arxiv.org/abs/1708.06189

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