The Sewing lemma for 0 < γ ≤ 1
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