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

Chaumont, L., Caravenna, F. (2013). An invariance principle for random walk bridges conditioned to stay positive. ELECTRONIC JOURNAL OF PROBABILITY, 18, 1-32 [10.1214/EJP.v18-2362].

An invariance principle for random walk bridges conditioned to stay positive

Caravenna, F
2013

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
Articolo in rivista - Articolo scientifico
Random Walk; Bridge; Excursion; Stable Law; Lévy Process; Conditioning to Stay Positive; Local Limit Theorem; Invariance Principle.
English
2013
18
1
32
none
Chaumont, L., Caravenna, F. (2013). An invariance principle for random walk bridges conditioned to stay positive. ELECTRONIC JOURNAL OF PROBABILITY, 18, 1-32 [10.1214/EJP.v18-2362].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/44605
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