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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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Contributor : Loïc Chaumont <>
Submitted on : Tuesday, October 9, 2012 - 9:42:43 PM
Last modification on : Friday, June 11, 2021 - 9:26:02 AM
Long-term archiving on: : Friday, December 16, 2016 - 10:25:08 PM


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  • HAL Id : hal-00691962, version 2



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



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