Paracontrolled calculus and regularity structures

2018/12/19 by Ismaël Bailleul, Bailleul, I., Masato Hoshino +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1812.07919

openalex publication_date 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the space of admissible models.

Citations

• An analytic BPHZ theorem for regularity structures
• An elementary proof of the reconstruction theorem
• Algebraic renormalisation of regularity structures

Cited by

• Commutator estimates from a viewpoint of regularity structures

Related

• Paracontrolled calculus and regularity structures (II)
• A Littlewood-Paley description of modelled distributions
• High order paracontrolled calculus
• Local expansion properties of paracontrolled systems
• An elementary proof of the reconstruction theorem