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A functional limit convergence towards brownian excursion.

Sohier, Julien (2010-11), A functional limit convergence towards brownian excursion.. https://basepub.dauphine.fr/handle/123456789/5242

Type
Document de travail / Working paper
External document link
http://hal.archives-ouvertes.fr/hal-00541530/fr/
Date
2010-11
Publisher
Université Paris Dauphine
Published in
Paris
Pages
22
Metadata
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Author(s)
Sohier, Julien
Abstract (EN)
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.
Subjects / Keywords
Invariance Principle; Conditioning to stay positive; Random walks