English

A functional limit convergence towards brownian excursion

Probability 2010-12-02 v1

Abstract

We consider a random walk SS in the domain of attraction of a standard normal law ZZ, \textit{ie} there exists a positive sequence ana_n such that Sn/anS_n/a_n converges in law towards ZZ. The main result of this note is that the rescaled process (Snt/an,t0)(S_{\lfloor nt \rfloor}/a_n, t \geq 0) conditioned to stay non-negative, to start and to come back \textit{near the origin} converges in law towards the normalized brownian excursion.

Keywords

Cite

@article{arxiv.1012.0118,
  title  = {A functional limit convergence towards brownian excursion},
  author = {Julien Sohier},
  journal= {arXiv preprint arXiv:1012.0118},
  year   = {2010}
}
R2 v1 2026-06-21T16:51:40.987Z