129 citations · 316 across the 45 of their papers we have counts for
28 papers · 1 filter
Chain rule symmetry for singular SPDEs from multi-indices to decorated trees
Yvain Bruned
In these lecture notes, we review the recent results around the chain rule for the generalised KPZ equation and the geometric KPZ equation. We introduce the main ideas of Regularit…
A general paracontrolled ansatz for singular SPDEs
Yvain Bruned, Nicolas Moench
We provide a general ansatz for the paracontrolled approach introduced by Gubinelli, Imkeller, Perkowski for treating singular SPDEs. The ansatz proposed covers a large class of eq…
Recentering with Malliavin derivative
Yvain Bruned, Aurélien Minguella
We provide an algebraic unification of the spectral gap proofs of the convergence of the renormalised model for regularity structures. We show that the key recentering map used in…
Banach fixed point and flow approach for rough analysis
Yvain Bruned, Yingtong Hou, Paul Laubie +1
In this paper, we show that the main algebraic assumption required to perform a fixed point argument for rough differential equations implies the algebraic assumption for the Baill…
Renormalisation in the flow approach for singular SPDEs
Yvain Bruned, Aurélien Minguella
In this work, we study the renormalisation of singular SPDEs in the flow approach recently developed by Duch. We introduce a general ansatz based on decorated trees for the solutio…
Flows driven by multi-indices Rough Paths
Carlo Bellingeri, Yvain Bruned, Yingtong Hou
In this work, we introduce a solution theory for scalar-valued rough differential equations driven by multi-indices rough paths. To achieve this task, we will show how the flow app…
Symmetries for the gKPZ equation via multi-indices
Carlo Bellingeri, Yvain Bruned
In this work, we study the two main symmetries for the one-dimensional generalised KPZ equation (gKPZ): the chain rule and the Itô Isometry. We consider the equation in the full-su…
Multi-indices coproducts from ODEs to singular SPDEs
Yvain Bruned, Yingtong Hou
In this work, we introduce explicit formulae for the coproducts at play for multi-indices in ODEs and in singular SPDEs. The two coproducts described correspond to versions of the…
Chain rule symmetry for singular SPDEs
Yvain Bruned, Vladimir Dotsenko
We characterise the chain rule symmetry for the geometric stochastic heat equations in the full subcritical regime for Gaussian and non-Gaussian noises. We show that the renormalis…
Quasi-generalised KPZ equation
Yvain Bruned, Máté Gerencsér, Usama Nadeem
We derive the renormalised equation for the quasi-generalised KPZ equation with space-time white noise. We complement the program initiated by Gerencsér and Hairer for solving quas…
Composition and substitution of Regularity Structures B-series
Yvain Bruned
In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define compositi…
A top-down approach to algebraic renormalization in regularity structures based on multi-indices
Yvain Bruned, Pablo Linares
We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``…
Random models for singular SPDEs
I. Bailleul, Y. Bruned
We give a proof of the convergence of the BHZ renormalized model associated with the generalized (KPZ) equation that does not require the full strength of the BPHZ renormalisation.…
Geometric embedding for regularity structures
Yvain Bruned, Foivos Katsetsiadis
In this paper, we show how one can view certain models in regularity structures as some form of geometric rough paths. This is performed by identifying the deformed Butcher-Connes-…
Diagram-free approach for convergence of tree-based models in Regularity Structures
Yvain Bruned, Usama Nadeem
In this work, we translate at the level of decorated trees some of the crucial arguments which have been used in arXiv:2112.10739 for proposing a diagram-free approach for the conv…
Post-Lie algebras in Regularity Structures
Yvain Bruned, Foivos Katsetsiadis
In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show…
Convergence of space-discretised gKPZ via Regularity Structures
Yvain Bruned, Usama Nadeem
In this work, we show a convergence result for the discrete formulation of the generalised KPZ equation ,…
Approximations of dispersive PDEs in the presence of low-regularity randomness
Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz
We introduce a new class of numerical schemes which allow for low regularity approximations to the expectation , where denotes the -th Four…
Parametrization of renormalized models for singular stochastic PDEs
I. Bailleul, Y. Bruned
Let be the regularity structure associated with a given system of singular stochastic PDEs. The paracontrolled representation of the map provides a linear par…
Ramification of Volterra-type Rough Paths
Yvain Bruned, Foivos Katsetsiadis
We extend the new approach introduced in arXiv:1912.02064v2 [math.PR] and arXiv:2102.10119v1 [math.PR] for dealing with stochastic Volterra equations using the ideas of Rough Path…
Renormalised singular stochastic PDEs
Ismael Bailleul, Yvain Bruned
Extended decorations on naturally decorated trees were introduced in the work of Bruned, Hairer and Zambotti on algebraic renormalization of regularity structures to provide a conv…
Algebraic deformation for (S)PDEs
Yvain Bruned, Dominique Manchon
We introduce a new algebraic framework based on the deformation of pre-Lie products. This allows us to provide a new construction of the algebraic objects at play in Regularity Str…
Renormalisation from non-geometric to geometric rough paths
Yvain Bruned
The Hairer-Kelly map has been introduced for establishing a correspondence between geometric and non-geometric rough paths. Recently, a new renormalisation on rough paths has been…
Bogoliubov type recursions for renormalisation in regularity structures
Yvain Bruned, Kurusch Ebrahimi-Fard
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are centr…