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A functional limit convergence towards brownian excursion.

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Date
2010-11
Publisher city
Paris
Publisher
Université Paris Dauphine
Link to item file
http://hal.archives-ouvertes.fr/hal-00541530/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
Invariance Principle; Conditioning to stay positive; Random walks
URI
https://basepub.dauphine.fr/handle/123456789/5242
Collections
  • CEREMADE : Publications
Metadata
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Author
Sohier, Julien
Type
Document de travail / Working paper
Item number of pages
22
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.

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