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Local asymptotics for the area under the random walk excursion
Published online by Cambridge University Press: 26 July 2018
Abstract
We study the 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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- Copyright © Applied Probability Trust 2018
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