[Grandes déviations et propriétés trajectorielles du « vrai » processus auto-répulsif]
We derive some large deviation bounds for events related to the “true self-repelling motion,” a one-dimensional self-interacting process introduced by Tóth and Werner, that has very different path properties than usual diffusion processes. We then use these estimates to study certain of these path properties such as its law of iterated logarithms for both small and large times.
Nous montrons dans cet article certaines bornes de grandes déviations pour des événements liés au « vrai » processus auto-répulsif, un processus unidimensionnel introduit par Toth et Werner, qui a des propriétés trajectorielles très différentes de celles des diffusions usuelles. Nous utilisons ensuite ces estimées pour étudier certaines de ces propriétés trajectorielles concernant la loi du logarithme itéré pour les petits temps ainsi que les grands temps.
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DOI : 10.24033/bsmf.2756
Keywords: True self-repelling motion, Brownian web, self-interacting processes, local time, large deviations, law of the iterated logarithm.
Mots-clés : Vrai processus auto-répulsif, réseau brownien, processus auto-interagissant, temps local, larges déviations, loi du logarithme itéré.
Dumaz, Laure 1
@article{BSMF_2018__146_1_215_0,
author = {Dumaz, Laure},
title = {Large deviations and path properties of the true self-repelling motion},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {215--240},
year = {2018},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {146},
number = {1},
doi = {10.24033/bsmf.2756},
mrnumber = {3864874},
zbl = {1404.60039},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2756/}
}
TY - JOUR AU - Dumaz, Laure TI - Large deviations and path properties of the true self-repelling motion JO - Bulletin de la Société Mathématique de France PY - 2018 SP - 215 EP - 240 VL - 146 IS - 1 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2756/ DO - 10.24033/bsmf.2756 LA - en ID - BSMF_2018__146_1_215_0 ER -
%0 Journal Article %A Dumaz, Laure %T Large deviations and path properties of the true self-repelling motion %J Bulletin de la Société Mathématique de France %D 2018 %P 215-240 %V 146 %N 1 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2756/ %R 10.24033/bsmf.2756 %G en %F BSMF_2018__146_1_215_0
Dumaz, Laure. Large deviations and path properties of the true self-repelling motion. Bulletin de la Société Mathématique de France, Tome 146 (2018) no. 1, pp. 215-240. doi: 10.24033/bsmf.2756
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