2018/12/07 by Harprit Singh, Singh, Harprit, Josef Teichmann +1 · 2 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #60H15 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1812.03082
openalex publication_date 2018/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The reconstruction theorem, a cornerstone of Martin Hairer's theory of regularity structures, appears in this article as the unique extension of the explicitly given reconstruction operator on the set of smooth models due its inherent Lipschitz properties. This new proof is a direct consequence of constructions of mollification procedures on spaces of models and modelled distributions: more precisely, for an abstract model Z of a given regularity structure, a mollified model is constructed, and additionally, any modelled distribution f can be approximated by elements of a universal subspace of modelled distribution spaces. These considerations yield in particular a non-standard approximation results for rough path theory. All results are formulated in a generic (p,q) Besov setting.