# A functional limit convergence towards brownian excursion.

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 $S {\lfloor nt floor}-a n, t \geq 0$ conditioned to stay non-negative, to start and to come back \textit{near the origin} converges in law towards the normalized brownian excursion.

Keywords : Invariance Principle Random walks Conditioning to stay positive Invariance Principle.

Author: Julien Sohier -

Source: https://hal.archives-ouvertes.fr/