English

Local asymptotics for the area under the random walk excursion

Probability 2017-08-22 v1

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.

Keywords

Cite

@article{arxiv.1708.06189,
  title  = {Local asymptotics for the area under the random walk excursion},
  author = {Elena Perfilev and Vitali Wachtel},
  journal= {arXiv preprint arXiv:1708.06189},
  year   = {2017}
}

Comments

22 pages

R2 v1 2026-06-22T21:19:27.210Z