Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Yvain Bruned"'
Autor:
Yvain Bruned, Foivos Katsetsiadis
Publikováno v:
Forum of Mathematics, Sigma, Vol 11 (2023)
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 that this can be done using either of the two combinatorial structure
Externí odkaz:
https://doaj.org/article/471462529e014520acf1504f6884d972
Autor:
Yvain Bruned, Katharina Schratz
Publikováno v:
Forum of Mathematics, Pi, Vol 10 (2022)
We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the partial differential equation (PDE) and to approximate
Externí odkaz:
https://doaj.org/article/2ab1212fe5394feea754a1aba29d07e6
Publikováno v:
Bruned, Y, Chandra, A, Chevyrev, I & Hairer, M 2020, ' Renormalising SPDEs in regularity structures ', Journal of the European Mathematical Society, vol. 23, no. 3, pp. 869–947 . https://doi.org/10.4171/JEMS/1025
The formalism recently introduced in arXiv:1610.08468 allows one to assign a regularity structure, as well as a corresponding "renormalisation group", to any subcritical system of semilinear stochastic PDEs. Under very mild additional assumptions, it
Publikováno v:
EMS Newsletter
EMS Newsletter, European Mathematical Society, 2020, 2020-3 (115), pp.7-11. ⟨10.4171/NEWS/115/3⟩
EMS Newsletter, European Mathematical Society, 2020, 2020-3 (115), pp.7-11. ⟨10.4171/NEWS/115/3⟩
International audience
Publikováno v:
Bruned, Y, Curry, C & Ebrahimi-Fard, K 2019, ' Quasi-shuffle algebras and renormalisation of rough differential equations ', Bulletin of the london mathematical society, vol. 52, no. 1, pp. 43-63 . https://doi.org/10.1112/blms.12305
The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on rooted trees known from backward error analysis of $B$-series. For this p
Publikováno v:
Bruned, Y, Hairer, M & Zambotti, L 2019, ' Algebraic renormalisation of regularity structures ', Inventiones mathematicae, vol. 215, no. 3, pp. 1039-1156 . https://doi.org/10.1007/s00222-018-0841-x
Inventiones Mathematicae
Inventiones Mathematicae, Springer Verlag, 2019, 215 (3), pp.1039-1156. ⟨10.1007/s00222-018-0841-x⟩
Inventiones Mathematicae
Inventiones Mathematicae, Springer Verlag, 2019, 215 (3), pp.1039-1156. ⟨10.1007/s00222-018-0841-x⟩
We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which comes with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4be5e3b253b11ce7b689099e8cbb6bca
https://hdl.handle.net/20.500.11820/76753587-e0e6-4db2-bdff-bb9da052490c
https://hdl.handle.net/20.500.11820/76753587-e0e6-4db2-bdff-bb9da052490c
Publikováno v:
Bruned, Y, Gabriel, F, Hairer, M & Zambotti, L 2021, ' Geometric stochastic heat equations ', Journal of the american mathematical society, vol. 35, pp. 1-80 . https://doi.org/10.1090/jams/977
Bruned, Y, Gabriel, F, Hairer, M & Zambotti, L 2019 ' Geometric stochastic heat equations ' . < https://arxiv.org/abs/1902.02884 >
Bruned, Y, Gabriel, F, Hairer, M & Zambotti, L 2019 ' Geometric stochastic heat equations ' . < https://arxiv.org/abs/1902.02884 >
We consider a natural class of $\mathbf{R}^d$-valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorphism group on $\mathbf{R}^d$. This class contains in particular the KPZ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d7c7fb2c05b4a21fa9ad664cb6be5a3a
Autor:
Yvain Bruned
Publikováno v:
Bruned, Y 2018, ' Recursive formulae in regularity structures ', Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, no. 4, pp. 525-564 . https://doi.org/10.1007/s40072-018-0115-z
We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far with the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f422c4f3101b8fc2f189e59ea66ff299
https://hdl.handle.net/20.500.11820/811713e7-033b-4a11-bfc8-e99d44f8b4e6
https://hdl.handle.net/20.500.11820/811713e7-033b-4a11-bfc8-e99d44f8b4e6
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783319749280
We demonstrate two examples of stochastic processes whose lifts to geometric rough paths require a renormalisation procedure to obtain convergence in rough path topologies. Our first example involves a physical Brownian motion subject to a magnetic f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3f4c170193b88d9a2790acf1f42958d4
Publikováno v:
Journal of Functional Analysis
Bruned, Y, Chevyrev, I, Friz, P K & Preiss, R 2019, ' A rough path perspective on renormalization ', Journal of functional analysis, vol. 277, no. 11, 108283 . https://doi.org/10.1016/j.jfa.2019.108283
Bruned, Y, Chevyrev, I, Friz, P K & Preiss, R 2019, ' A rough path perspective on renormalization ', Journal of functional analysis, vol. 277, no. 11, 108283 . https://doi.org/10.1016/j.jfa.2019.108283
We develop the algebraic theory of rough path translation. Particular attention is given to the case of branched rough paths, whose underlying algebraic structure (Connes-Kreimer, Grossman-Larson) makes it a useful model case of a regularity structur
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e91764d25bd756f354e9ea2fbc2adc0