A functional limit convergence towards brownian excursion
Probability
2010-12-02 v1
Abstract
We consider a random walk in the domain of attraction of a standard normal law , \textit{ie} there exists a positive sequence such that converges in law towards . The main result of this note is that the rescaled process conditioned to stay non-negative, to start and to come back \textit{near the origin} converges in law towards the normalized brownian excursion.
Cite
@article{arxiv.1012.0118,
title = {A functional limit convergence towards brownian excursion},
author = {Julien Sohier},
journal= {arXiv preprint arXiv:1012.0118},
year = {2010}
}