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 $(S_{ \lfloor nt \rfloor}/a_n, t \geq 0)$ conditioned to stay non-negative, to start and to come back \textit{ near the origin} converges in law towards the normalized brownian excursion.
Categories: math.PR