A central limit theorem for two-dimensional random walks in a cone
Bulletin de la Société Mathématique de France, Volume 139 (2011) no. 2, p. 271-286

We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.

Nous démontrons qu'une marche aléatoire dans le plan, centrée, à accroissements bornés, et conditionnée à rester dans un cône, converge en loi vers le méandre brownien correspondant si et seulement si la queue de la loi du temps de sortie du cône est à variation régulière. Cette condition est satisfaite dans de nombreux exemples naturels.

DOI : https://doi.org/10.24033/bsmf.2608
Classification:  60F17,  60G50,  60J05,  60J65
Keywords: conditioned random walks, brownian motion, brownian meander, cone, functional limit theorem, regularly varying sequences
@article{BSMF_2011__139_2_271_0,
     author = {Garbit, Rodolphe},
     title = {A central limit theorem for two-dimensional random walks in a cone},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {139},
     number = {2},
     year = {2011},
     pages = {271-286},
     doi = {10.24033/bsmf.2608},
     zbl = {1217.60026},
     mrnumber = {2828570},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2011__139_2_271_0}
}
Garbit, Rodolphe. A central limit theorem for two-dimensional random walks in a cone. Bulletin de la Société Mathématique de France, Volume 139 (2011) no. 2, pp. 271-286. doi : 10.24033/bsmf.2608. http://www.numdam.org/item/BSMF_2011__139_2_271_0/

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