A functional limit convergence towards brownian excursion

Abstract

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

References in corpus (1)

• Invariance principles for random walks conditioned to stay positive