N. Remerciements, L. Victoir, S. Coutin, M. Tindel, J. Gubinelli et al., auteur tient à remercier ici tous ceux qui l'ont aidé dans l'exploration de cette théorie, en premier lieu T, ainsi que les très nombreuses personnes avec lesquelles il a échangé au cours de visites, conférences et séminaires

I. Bailleul, Flows driven by rough paths, Revista Matem??tica Iberoamericana, vol.31, issue.3, 2012.
DOI : 10.4171/RMI/858
URL : https://hal.archives-ouvertes.fr/hal-00704959

F. Baudoin, An Introduction to the Geometry of Stochastic Flows, 2004.

S. Blanes, F. Cases, J. A. Oteo, and J. Ros, The Magnus expansion and some of its applications, Physics Reports, vol.470, issue.5-6, pp.151-238, 2009.
DOI : 10.1016/j.physrep.2008.11.001

K. Chen, Integration of paths???a faithful representation of paths by non-commutative formal power series, Transactions of the American Mathematical Society, vol.89, issue.2, pp.395-407, 1958.
DOI : 10.1090/S0002-9947-1958-0106258-0

L. Coutin and Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions, Probability Theory and Related Fields, vol.122, issue.1, pp.108-140, 2002.
DOI : 10.1007/s004400100158
URL : https://hal.archives-ouvertes.fr/hal-00266874

A. M. Davie, Differential Equations Driven by Rough Signals : an Approach via Discrete Approximation, Appl. Math. Res. Express. AMRX, vol.2, p.40, 2007.

D. Feyel, A. De-la-pradelle, and G. Mokobodzki, A non-commutative sewing lemma, Electronic Communications in Probability, vol.13, issue.0, pp.24-34, 2008.
DOI : 10.1214/ECP.v13-1345
URL : https://hal.archives-ouvertes.fr/hal-00151183

D. Feyel, A. De, and L. Pradelle, Curvilinear integrals along enriched paths, Electron, J. Probab, vol.11, issue.34, pp.860-892, 2006.

P. Friz and N. Victoir, Multidimensional Stochastic Processes as Rough Paths Theory and Applications A note on the notion of geometric rough paths, Probab. Theory Related Fields, vol.10, issue.136 3, pp.395-416, 2006.

J. G. , L. Gaines, and T. J. , Variable step size control in the numerical solution of stochastic differential equations, SIAM J. Appl. Math, vol.57, issue.5, pp.1455-1484, 1997.

M. Gubinelli, Controlling rough paths, Journal of Functional Analysis, vol.216, issue.1, pp.86-140, 2004.
DOI : 10.1016/j.jfa.2004.01.002
URL : http://doi.org/10.1016/j.jfa.2004.01.002

M. Hairer, Solving the KPZ equation, 2011.

M. Ledoux, Z. Qian, and T. Zhang, Large deviations and support theorem for diffusion processes via rough paths, Stochastic Process, Appl, vol.102, issue.2, pp.265-283, 2002.

A. Lejay, Controlled differential equations as Young integrals: A simple approach, Yet another introduction to rough paths, pp.215-246, 2009.
DOI : 10.1016/j.jde.2010.05.006
URL : https://hal.archives-ouvertes.fr/inria-00402397

A. Lejay and N. Victoir, On <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-rough paths, Journal of Differential Equations, vol.225, issue.1, pp.103-133, 2006.
DOI : 10.1016/j.jde.2006.01.018

A. Lejay, An Introduction to Rough Paths, Lecture Notes in Math, vol.1832, pp.1-59, 2003.
DOI : 10.1007/978-3-540-40004-2_1
URL : https://hal.archives-ouvertes.fr/inria-00102184

T. J. Lyons, Differential equations driven by rough signals, Revista Matem??tica Iberoamericana, vol.14, issue.2, pp.215-310, 1998.
DOI : 10.4171/RMI/240

T. Lyons, M. Caruana, and T. Lévy, Differential Equations Driven by Rough Paths, École d'été des probabilités de Saint-Flour XXXIV ?, Lecture Notes in Math, vol.1908, 2004.

T. Lyons and Z. Qian, System Control and Rough Paths, 2002.

T. Lyons and N. Victoir, An extension theorem to rough paths, Cubature on Wiener space, pp.835-847, 2004.
DOI : 10.1016/j.anihpc.2006.07.004

J. Magnen and J. Unterberger, From Constructive Field Theory to Fractional Stochastic Calculus. (I) An introduction: Rough Path Theory and Perturbative Heuristics, Annales Henri Poincar??, vol.36, issue.1, pp.1199-1226, 2011.
DOI : 10.1007/s00023-011-0106-3
URL : https://hal.archives-ouvertes.fr/hal-00491768

G. Pagès and A. Sellami, Convergence of Multi-Dimensional Quantized SDE???s, Lecture Notes in Math, vol.2006, pp.269-307, 2011.
DOI : 10.1007/978-3-642-15217-7_11

J. Unterberger, Aspects de la théorie des chemins rugueux, Gazette des mathématiciens, vol.131, pp.16-33, 2012.

L. C. Young, 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