The Sewing lemma for 0 < γ ≤ 1

Journal of Functional Analysis - Tập 283 - Trang 109644 - 2022
Lucas Broux1, Lorenzo Zambotti1
1Sorbonne Université, Université de Paris Cité, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, 4 Pl. Jussieu, 75005 Paris, France

Tài liệu tham khảo

Boedihardjo, 2019, An isomorphism between branched and geometric rough paths, Ann. Inst. Henri Poincaré Probab. Stat., 55, 1131, 10.1214/18-AIHP912 Bahouri, 2011, Fourier Analysis and Nonlinear Partial Differential Equations, vol. 343 Bellingeri Bellingeri Bailleul, 2021, Paracontrolled calculus and regularity structures I, J. Math. Soc. Jpn., 73, 553, 10.2969/jmsj/81878187 Bailleul, 2021, Paracontrolled calculus and regularity structures II, J. Éc. Polytech. Math., 8, 1275, 10.5802/jep.172 Brault, 2019, Solving rough differential equations with the theory of regularity structures, vol. 2252, 127 Cartier, 2007, A primer of Hopf algebras, 537 Curry, 2020, Planarly branched rough paths and rough differential equations on homogeneous spaces, J. Differ. Equ., 269, 9740, 10.1016/j.jde.2020.06.058 Chen, 1954, Iterated integrals and exponential homomorphisms, Proc. Lond. Math. Soc. (3), 4, 502, 10.1112/plms/s3-4.1.502 Cartier, 2021 Caravenna, 2020, Hairer's reconstruction theorem without regularity structures, EMS Surv. Math. Sci., 7, 207, 10.4171/EMSS/39 Deya, 2013, On the rough-paths approach to non- commutative stochastic calculus, J. Funct. Anal., 265, 594, 10.1016/j.jfa.2013.04.008 Delarue Friz, 2020, A Course on Rough Paths, 10.1007/978-3-030-41556-3 Feyel, 2006, Curvilinear integrals along enriched paths, Electron. J. Probab., 11, 860 Feyel, 2008, A non-commutative sewing lemma, Electron. Commun. Probab., 13, 24, 10.1214/ECP.v13-1345 Friz Gubinelli, 2004, Controlling rough paths, J. Funct. Anal., 216, 86, 10.1016/j.jfa.2004.01.002 Gubinelli, 2010, Ramification of rough paths, J. Differ. Equ., 248, 693, 10.1016/j.jde.2009.11.015 Hairer, 2014, A theory of regularity structures, Invent. Math., 198, 269, 10.1007/s00222-014-0505-4 Hairer, 2015, Geometric versus non-geometric rough paths, Ann. Inst. Henri Poincaré Probab. Stat., 51, 207, 10.1214/13-AIHP564 Kondurar, 1937, Sur l'intégrale de Stieltjes, Rec. Math. Moscou, Ser 2, 44, 361 Linares Lyons, 2007, An extension theorem to rough paths, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 24, 835, 10.1016/j.anihpc.2006.07.004 Lyons, 1998, Differential equations driven by rough signals, Rev. Mat. Iberoam., 14, 215, 10.4171/RMI/240 Lê, 2020, A stochastic sewing lemma and applications, Electron. J. Probab., 25, 10.1214/20-EJP442 Milnor, 1965, On the structure of Hopf algebras, Ann. Math. (2), 81, 211, 10.2307/1970615 Nualart, 2011, A construction of the rough path above fractional Brownian motion using Volterra's representation, Ann. Probab., 39, 1061, 10.1214/10-AOP578 Reutenauer, 2003, Free Lie algebras, 887, 10.1016/S1570-7954(03)80075-X Tapia, 2020, The geometry of the space of branched rough paths, Proc. Lond. Math. Soc. (3), 121, 220, 10.1112/plms.12311 Unterberger, 2010, Hölder-continuous rough paths by Fourier normal ordering, Commun. Math. Phys., 298, 1, 10.1007/s00220-010-1064-1 Unterberger, 2013, A renormalized rough path over fractional Brow nian motion, Commun. Math. Phys., 320, 603, 10.1007/s00220-013-1707-0 Young, 1936, An inequality of the Hölder type, connected with Stieltjes integration, Acta Math., 67, 251, 10.1007/BF02401743 Zorin-Kranich