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An invariance principle for random walk bridges conditioned to stay positive


 
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1. Title Title of document An invariance principle for random walk bridges conditioned to stay positive
 
2. Creator Author's name, affiliation, country Francesco Caravenna; Università degli Studi di Milano-Bicocca; Italy
 
2. Creator Author's name, affiliation, country Loïc Chaumont; Université d'Angers; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random Walk, Bridge, Excursion, Stable Law, Lévy Process, Conditioning to Stay Positive, Local Limit Theorem, Invariance Principle.
 
3. Subject Subject classification 60G50, 60G51, 60B10
 
4. Description Abstract We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes as a special case the convergence under diffusive rescaling of random walk excursions toward the normalized Brownian excursion, for zero mean, finite variance random walks. The proof exploits asuitable absolute continuity relation together with some local asymptotic estimates for random walks conditioned to stay positive, recently obtained by Vatutin and Wachtel and by Doney.We review and extend these relations to the absolutely continuous setting.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ERC VARIS 267356; ANR-09-BLANC-0084-01; ECOS-CONACYT CNRS Research project M07-M01
 
7. Date (YYYY-MM-DD) 2013-06-05
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2362
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2362
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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