, Differential equations driven by rough signals, Revista Matem??tica Iberoamericana, vol.14, issue.2, pp.215-310, 1998.
DOI : 10.4171/RMI/240
, System Control and Rough Paths, 2002.
, An Introduction to Rough Paths, Lecture Notes in Mathematics, vol.1832, pp.1-59, 2003.
DOI : 10.1007/978-3-540-40004-2_1
URL : https://hal.archives-ouvertes.fr/inria-00102184
, Differential Equations Driven by Rough Paths, École d'été des probabilités de Saint-Flour XXXIV ?, Lecture Notes in Math, vol.1908, 2004.
, Yet another introduction to rough paths, Lecture Notes in Mathematics, 2009.
DOI : 10.1007/978-3-642-01763-6_1
URL : https://hal.archives-ouvertes.fr/inria-00107460
, Multidimensional Stochastic Processes as Rough Paths, Theory and Applications, 2009.
DOI : 10.1017/CBO9780511845079
, An introduction to the geometry of stochastic flows This in not a book about rough paths, but it gives some nice insight about the algebraic and geometric structure used the the theory of rough paths, 2004.
, The Magnus expansion and some of its applications, Phys, pp.151-238, 2009.
, Controlling rough paths, Journal of Functional Analysis, vol.216, issue.1, pp.86-140, 2004.
DOI : 10.1016/j.jfa.2004.01.002
, Curvilinear integrals along enriched paths, Electron, J. Probab, vol.11, issue.35, pp.860-892, 2006.
, Rough path analysis via fractional calculus, Transactions of the American Mathematical Society, vol.361, issue.05, pp.2689-2718, 2009.
DOI : 10.1090/S0002-9947-08-04631-X
, An inequality of the H??lder type, connected with Stieltjes integration, Acta Mathematica, vol.67, issue.0, pp.251-282, 1936.
DOI : 10.1007/BF02401743
, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré Sect. B (N.S.), vol.13, issue.2, pp.99-125, 1977.
, On the Gap Between Deterministic and Stochastic Ordinary Differential Equations, The Annals of Probability, vol.6, issue.1, pp.19-41, 1978.
DOI : 10.1214/aop/1176995608
, Controlled differential equations as Young integrals: a simple approach available at hal:inria-00402397. This article covers many results (existence, uniqueness, continuity, ...) on rough differential equations driven by paths, 2009.
, An introduction to (stochastic) calculus with respect fo fractional Brownian motion, pp.3-65, 2007.
, Stochastic calculus for fractional Brownian motion and related processes, Lecture Notes in Mathematics, vol.1929, 2008.
, Stochastic analysis, rough path analysis and fractional Brownian motions This article shows existence of iterated integrals for the fBM with H > 1/4 and the non existence of such integrals when H < 1/4 as a limit of piecewise linear approximations of the path, Probab. Theory Related Fields, vol.12240, issue.41, pp.108-140, 2002.
, Large deviations for rough paths of the fractional Brownian motion, This article shows a large deviation principle for the fBM, pp.245-271, 2006.
DOI : 10.1016/j.anihpb.2005.04.003
URL : https://hal.archives-ouvertes.fr/hal-00003655
, Operators associated with stochastic differential equations driven by fractional Brownian motions, Stochastic Proces, Appl, vol.117, issue.5, pp.550-574, 2007.
, These articles [29, 30] study the properties in small time of the semi-group associated to a SDE driven by a fBM using some algebraic properties on controlled differential equations and differential equations on Lie group, pp.1120-1139, 2008.
, A version of Hörmander's theorem for the fractional Brownian motion, Probab. Theory Related Fields, vol.139, pp.3-4, 2007.
, Approximation of rough paths of fractional Brownian motion, Seminar on Stochastic Analysis, Random Fields and Applications V, Progr. Probab, vol.59, pp.275-303, 2008.
, Good rough path sequences and applications to anticipating stochastic calculus, This article shows that the fBM solves some anticipative stochastic differential equation, pp.1172-1193, 2007.
DOI : 10.1214/009117906000000827
URL : https://hal.archives-ouvertes.fr/hal-00635592
, Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a??Fractional Brownian Motion, Journal of Theoretical Probability, vol.9, issue.1, pp.871-899, 2007.
DOI : 10.1007/s10959-007-0083-0
URL : https://hal.archives-ouvertes.fr/hal-00204490
, The rough path associated to the multidimensional analytic fbm with any Hurst parameter available at hal:hal-00327355. This article shows the existence of a rough path can be constructed for any value of H by using an analytical rough path proposed by, 2008.
, Delay equations driven by rough paths, Electron, J. Probab, vol.13, issue.67, pp.2031-2068, 2008.
, Some Differential Systems Driven by a fBm with Hurst Parameter Greater than 1/4, 2009.
DOI : 10.1007/978-3-642-29982-7_8
URL : https://hal.archives-ouvertes.fr/hal-00352998
, ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING, Stochastics and Dynamics, vol.09, issue.03, p.809, 2000.
DOI : 10.1142/S0219493709002737
URL : https://hal.archives-ouvertes.fr/hal-00320735
, Stochastic calculus for fractional Brownian motion with Hurst exponent H >??: A rough path method by analytic extension, The Annals of Probability, vol.37, issue.2, pp.565-614, 2009.
DOI : 10.1214/08-AOP413
URL : https://hal.archives-ouvertes.fr/hal-00147538
, Convergence of multi-dimensional quantized SDE's (2008), available at arxiv:0801.0726. This article develops a way of approximating a solution of some SDE using quantization (i.e., the replacement of a random variable by a discrete one) of the coefficients in the Karhunen-Loève decomposition
, Weak approximation of a fractional SDE (2007), available at arxiv:0790.0805. This article studies an approximation of a fractional SDE when the fBM is approximated by a Kac-Stroock approximation
, Trees and asymptotic expansions for fractional stochastic differential equations, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.45, issue.1, pp.157-174, 2009.
DOI : 10.1214/07-AIHP159
URL : https://hal.archives-ouvertes.fr/hal-00379919
, This article was a first attempt to deal with Stochastic Partial Differential Equations driven by rough paths. Here, a notion of mild solution is developped which can be used for fractional noise with enough regularity, pp.307-326, 2006.
, The 1-d stochastic wave equation driven by a fractional Brownian motion, Stochastic Process, Appl, vol.117, issue.10, pp.1448-1472, 2007.
, Rough evolution equation available at arvix: 0803.0552. This article develops a notion of SPDE using the theory of rough paths and proposed as an example a SPDE driven by a space-time fractional Brownian motion, 2008.
, Differential equations driven by Gaussian signals, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.2, pp.707-0313, 2007.
DOI : 10.1214/09-AIHP202
, available at arxiv:0711.0668. These articles [53, 54] relates the regularity of a Gaussian process to the covariance function and construct a rough path using the Karhunen-Loève decomposition, Differential Equations Driven by Gaussian Signals II, 2007.
, available at doi:10.1051/ps:2008007. This article also uses the Karhunen-Loève decomposition to construct an approximation of some Gaussian process and shows results of Wong-Zakai type, Stat, vol.13, pp.247-269, 2009.