Local asymptotics for the area under the random walk excursion-Reference-Cited by-同舟云学术

Local asymptotics for the area under the random walk excursion

Published:2018-06 Issue:2 Volume:50 Page:600-620
ISSN:0001-8678
Container-title:Advances in Applied Probability
language:en
Short-container-title:Adv. Appl. Probab.

Author:

Perfilev Elena,Wachtel Vitali

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference15 articles.

1. On the probability that integrated random walks stay positive

2. Local probabilities for random walks conditioned to stay positive

3. Sohier J. (2010). A functional limit convergence towards Brownian excursion. Preprint. Available at https://arxiv.org/abs/1012.0118.

4. On a random area variable arising in discrete-time queues and compact directed percolation

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Asymptotic results for certain first-passage times and areas of renewal processes;Theory of Probability and Mathematical Statistics;2023-05-02

2. Exact solution for the filling-induced thermalization transition in a one-dimensional fracton system;Physical Review B;2023-01-25

3. Hilbert space fragmentation produces an effective attraction between fractons;Physical Review Research;2022-01-26

4. Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments;Journal of Applied Probability;2021-02-25