[EDP stochastiques singulières de type champ moyen]
We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a propagation of chaos result.
Nous étudions un système de champs en interaction dont les évolutions sont données par des équations aux dérivées partielles stochastiques singulières de type champ moyen. Nous introduisons un cadre robuste pour l’étude de tels systèmes et de leurs dynamiques limites. Nous démontrons le caractère bien posé de ces équations et un théorème de propagation du chaos pour le système de champs en interaction.
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Keywords: Singular stochastic PDEs, mean field interaction, paracontrolled calculus
Mots-clés : Équations aux dérivées partielles stochastiques singulières, interaction de type champ moyen, calcul paracontrôlé
Ismaël Bailleul 1 ; Nicolas Moench 2
CC-BY 4.0
Ismaël Bailleul; Nicolas Moench. Mean field singular stochastic partial differential equations. Journal de l’École polytechnique — Mathématiques, Tome 13 (2026), pp. 1099-1149. doi: 10.5802/jep.344
@article{JEP_2026__13__1099_0,
author = {Isma\"el Bailleul and Nicolas Moench},
title = {Mean field singular stochastic partial~differential equations},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1099--1149},
year = {2026},
publisher = {\'Ecole polytechnique},
volume = {13},
doi = {10.5802/jep.344},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.344/}
}
TY - JOUR AU - Ismaël Bailleul AU - Nicolas Moench TI - Mean field singular stochastic partial differential equations JO - Journal de l’École polytechnique — Mathématiques PY - 2026 SP - 1099 EP - 1149 VL - 13 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.344/ DO - 10.5802/jep.344 LA - en ID - JEP_2026__13__1099_0 ER -
%0 Journal Article %A Ismaël Bailleul %A Nicolas Moench %T Mean field singular stochastic partial differential equations %J Journal de l’École polytechnique — Mathématiques %D 2026 %P 1099-1149 %V 13 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.344/ %R 10.5802/jep.344 %G en %F JEP_2026__13__1099_0
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