2021
DOI: 10.2969/jmsj/81878187
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Paracontrolled calculus and regularity structures I

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.

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Cited by 13 publications
(52 citation statements)
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“…The BPHZ renormalization procedure for the model involves a real-valued map k acting on a side space T − , which also defines a homogeneity-preserving linear map k from T into itself. It follows from [5,Th. 21] that the bracket data associated with the renormalized model k M ε is simply given by the [[ k(τ )]], for τ of negative homogeneity.…”
Section: Introductionmentioning
confidence: 93%
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“…The BPHZ renormalization procedure for the model involves a real-valued map k acting on a side space T − , which also defines a homogeneity-preserving linear map k from T into itself. It follows from [5,Th. 21] that the bracket data associated with the renormalized model k M ε is simply given by the [[ k(τ )]], for τ of negative homogeneity.…”
Section: Introductionmentioning
confidence: 93%
“…It happens nonetheless to be possible to compare the two languages, independently of their applications to the study of singular stochastic PDEs. This task was initiated in Gubinelli, Imkeller, Perkowski' seminal work [13] and Martin and Perkowski's work [22], and in our previous work [5], where we proved that the set of admissible models M = (g, Π) over a concrete regularity structure T = (T + , ∆ + ), (T, ∆) equipped with an abstract integration map is parameterized by a paracontrolled representation of Π on the set of elements τ with non-positive homogeneity. (Admissible models play a crucial in the regularity structures approach to the study of singular stochastic PDEs.)…”
Section: Introductionmentioning
confidence: 99%
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