A functional limit convergence towards brownian excursion.

Julien Sohier (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Invariance Principle; Random walks; Conditioning to stay positive; Invariance Principle.

Domaines: Probabilités [math.PR]

Julien Sohier. A functional limit convergence towards brownian excursion.. 2010. ⟨hal-00541530⟩