An invariance principle for random walk bridges conditioned to stay positive

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 a suitable absolute continuity relation together with some local asymptotic estimates for random walks conditioned to stay positive, recently obtained by Vatutin and Wachtel [38] and Doney [21].We review and extend these relations to the absolutely continuous setting.
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Pré-publication, Document de travail
2012
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https://hal.archives-ouvertes.fr/hal-00691962
Contributeur : Loïc Chaumont <>
Soumis le : mardi 9 octobre 2012 - 21:42:43
Dernière modification le : lundi 5 février 2018 - 15:00:03
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  • HAL Id : hal-00691962, version 2

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Francesco Caravenna, Loïc Chaumont. An invariance principle for random walk bridges conditioned to stay positive. 2012. 〈hal-00691962v2〉

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