A functional limit convergence towards brownian excursion
Abstract
We consider a random walk S in the domain of attraction of a standard normal law Z, ie there exists a positive sequence an such that Sn/an converges in law towards Z. The main result of this note is that the rescaled process (S nt /an, t ≥ 0) conditioned to stay non-negative, to start and to come back near the origin converges in law towards the normalized brownian excursion.
0