Invariance principles for random walks in cones

We prove invariance principles for a multidimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of h-transformed random walk to the corresponding h-transform of the Brownian...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 130; no. 7; pp. 3920 - 3942
Main Authors Duraj, Jetlir, Wachtel, Vitali
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2020
Subjects
Exit time
Invariance principle
Random walk
secondary
Invariance principle
Random walk
Exit time
primary
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Summary:We prove invariance principles for a multidimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of h-transformed random walk to the corresponding h-transform of the Brownian motion. Finally, we prove an invariance principle for bridges of a random walk in a cone.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2019.11.004