R. J. Adler, An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, Institute of Mathematical Statistics Lecture Notes-Monograph Series, vol.12, 1990.

F. Baudoin and M. Hairer, A Version of Hörmander's Theorem for the Fractional Brownian Motion. Probab. Theory Relat, pp.373-395, 2007.

F. Baudoin, C. Ouyang, and S. Tindel, Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.1, 2012.
DOI : 10.1214/12-AIHP522

R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, 2001.
DOI : 10.1090/chel/344

M. Besalu and D. Nualart, ESTIMATES FOR THE SOLUTION TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H ??? (???, ??), Stochastics and Dynamics, vol.11, issue.02n03, pp.243-263, 2011.
DOI : 10.1142/S0219493711003267

T. Cass, C. Litterer, and T. Lyons, Integrability and tail estimates for Gaussian rough differential equations, The Annals of Probability, vol.41, issue.4, 2011.
DOI : 10.1214/12-AOP821

K. T. Chen, Iterated Integrals and Exponential Homomorphisms, Proc. London Math. Soc, issue.3
DOI : 10.1007/978-1-4612-2096-1_5
URL : http://plms.oxfordjournals.org/cgi/content/short/s3-4/1/502

K. T. Chen, Algebraization of iterated integration along paths, Bulletin of the American Mathematical Society, vol.73, issue.6, pp.975-978, 1967.
DOI : 10.1090/S0002-9904-1967-11869-X

K. T. Chen, Iterated path integrals and generalized paths, Bulletin of the American Mathematical Society, vol.73, issue.6, pp.935-938, 1967.
DOI : 10.1090/S0002-9904-1967-11858-5

P. Cheridito, Regularizing Fractional Brownian Motion with a View towards Stock Prince Modeling, Thèse de doctorat de l'université de Zürich, 2001.

P. Cheridito, H. Kawaguchi, and M. Maejima, Fractional Ornstein-Uhlenbeck processes, Electronic Journal of Probability, vol.8, issue.0, pp.1-14, 2003.
DOI : 10.1214/EJP.v8-125

A. Chronopoulou and S. Tindel, On inference for fractional differential equations, Statistical Inference for Stochastic Processes, vol.111, issue.1, 2011.
DOI : 10.1007/s11203-013-9076-z
URL : https://hal.archives-ouvertes.fr/hal-00587087

S. Cohen and F. Panloup, Approximation of stationary solutions of Gaussian driven stochastic differential equations, Stochastic Processes and their Applications, pp.2776-2801, 2011.
DOI : 10.1016/j.spa.2011.08.001
URL : https://hal.archives-ouvertes.fr/hal-00441180

G. E. Correll and G. E. Futter, Two Case Studies of Patients with Major Depressive Disorder Given Low-Dose (Subanesthetic) Ketamine Infusions, Pain Medicine, vol.7, issue.1, 2006.
DOI : 10.1111/j.1526-4637.2006.00101.x

L. Coutin, Rough Paths via Sewing Lemma. ESAIM : Probability and Statistics, doi :10, 1051.

L. Coutin, P. Friz, and N. Victoir, Good rough path sequences and applications to anticipating stochastic calculus, The Annals of Probability, vol.35, issue.3, pp.1172-1193, 2007.
DOI : 10.1214/009117906000000827
URL : https://hal.archives-ouvertes.fr/hal-00635592

L. Coutin and A. Lejay, Semi-martingales and rough paths theory, Electronic Journal of Probability, vol.10, issue.0, pp.761-785, 2005.
DOI : 10.1214/EJP.v10-162
URL : https://hal.archives-ouvertes.fr/inria-00000411

L. Coutin and A. Lejay, Perturbed Linear Rough Differential Equations. INRIA :hal-00722900v1, 2012.
DOI : 10.5802/ambp.338
URL : https://hal.archives-ouvertes.fr/hal-00722900

L. Coutin and Z. Qian, Stochastic Analysis, Rough Path Analysis and Fractional Brownian Motions. Probab. Theory Related Fields, pp.108-140, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00266874

J. C. Cox, J. E. Ingersoll, and S. A. Ross, A Theory of the Term Structure of Interest Rates, Econometrica, vol.53, issue.2, pp.385-407, 1985.
DOI : 10.2307/1911242

A. M. Davie, Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation, Applied Mathematics Research eXpress, vol.40, issue.2, 2007.
DOI : 10.1093/amrx/abm009

L. Decreusefond and S. Ustunel, Stochastic Analysis of the Fractional Brownian Motion. Potential Anal, pp.177-214, 1999.

M. Delattre, Pharmacokinetics and Stochastic Differential Equations : Model and Methodology. 20th Meeting of the Population Approach Group in Europe, 2011.

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Applications of Mathematics, vol.38, 1998.
DOI : 10.1007/978-1-4612-5320-4

A. Deya, M. Gubinelli, and S. Tindel, Non-linear rough heat equations, Probability Theory and Related Fields, vol.239, issue.1, 2012.
DOI : 10.1007/s00440-011-0341-z
URL : https://hal.archives-ouvertes.fr/hal-00658081

A. Deya and S. Tindel, ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING, Stochastics and Dynamics, vol.09, issue.03, pp.437-477, 2009.
DOI : 10.1142/S0219493709002737
URL : https://hal.archives-ouvertes.fr/hal-00320735

A. Deya and S. Tindel, Rough Volterra equations 2: Convolutional generalized integrals, Stochastic Processes and their Applications, vol.121, issue.8, pp.1864-1899, 2011.
DOI : 10.1016/j.spa.2011.05.003
URL : https://hal.archives-ouvertes.fr/hal-00328409

T. Dieker, Simulation of Fractional Brownian Motion, 2004.

H. Doss, Liens entre équations différentielles stochastiques et ordinaires, C.R. Acad. Sci. Paris Ser. A-B, vol.283, issue.13, pp.939-942, 1976.

D. Feyel and A. De-la-pradelle, Curvilinear Integrals Along Enriched Paths, Electronic Journal of Probability, vol.11, issue.0, pp.860-892, 2006.
DOI : 10.1214/EJP.v11-356

J. Feng, J. Fouque, and R. Kumar, Small-time asymptotics for fast mean-reverting stochastic volatility models, The Annals of Applied Probability, vol.22, issue.4, pp.1541-1575, 2012.
DOI : 10.1214/11-AAP801

M. Fliess and D. Normand-cyrot, Alg??bres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et int??grales it??r??es de K. T. Chen, Séminaire de Probabilités XVI, pp.257-267, 1982.
DOI : 10.1007/BF00535284

E. Fournié, J. Lasry, J. Lebuchoux, P. Lions, and N. Touzi, Applications of Malliavin calculus to Monte Carlo methods in finance, Finance and Stochastics, vol.3, issue.4, pp.391-412, 1999.
DOI : 10.1007/s007800050068

P. Friz and N. Victoir, A Note on the Notion of Geometric Rough Paths. Probab. Theory Related Fields, pp.395-416, 2006.

P. Friz and N. Victoir, Differential equations driven by Gaussian signals, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.2, pp.369-410, 2010.
DOI : 10.1214/09-AIHP202

P. Friz and N. Victoir, The Burkholder-Davis-Gundy Inequality for Enhanced Martingales, Lecture Notes in Mathematics, vol.1934, 2008.
DOI : 10.1007/978-3-540-77913-1_20

P. Friz and N. Victoir, Multidimensional Stochastic Processes as Rough Paths : Theory and Applications, Cambridge Studies in Applied Mathematics, vol.120, 2010.
DOI : 10.1017/CBO9780511845079

E. Gobet and R. Münos, Sensitivity Analysis Using It??--Malliavin Calculus and Martingales, and Application to Stochastic Optimal Control, SIAM Journal on Control and Optimization, vol.43, issue.5, pp.1676-1713, 2005.
DOI : 10.1137/S0363012902419059

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 and A. Ohashi, Ergodic Theory for SDEs with Extrinsic Memory. The Annals of Probability, 1950.

Y. Hu and D. Nualart, Differential Equations Driven by H??lder Continuous Functions of Order Greater than 1/2, Stochast. Anal. Appl, vol.2, pp.399-413, 2007.
DOI : 10.1007/978-3-540-70847-6_17

K. Itô, Stochastic Integral, Proc. Imp. Acad. Tokyo, pp.519-524, 1944.

K. Itô, Stochastic Differential Equations, Memoirs AMS, vol.4, 1951.

J. Jacod, Calcul stochastique et problèmes de martingales, Lecture Notes in Mathematics, vol.714, 1979.
DOI : 10.1007/BFb0064907

K. Kalogeropoulos, N. Demiris, and O. Papaspiliopoulos, Diffusion-driven Models for Physiological Processes, International Workshop on Applied Probability, 2008.

S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, 1981.

Y. Khatib and N. Privault, Computations of Greeks in a market with jumps via the Malliavin calculus, Finance and Stochastics, vol.8, issue.2, pp.161-179, 2004.
DOI : 10.1007/s00780-003-0111-6

A. Kohatsu-higa and J. A. León, Anticipating Stochastic Differential Equations of Stratonovich Type, Applied Mathematics and Optimization, vol.36, issue.3, pp.263-289, 1997.
DOI : 10.1007/s002459900063

H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge Studies in Applied Mathematics, vol.24, 1997.

Y. A. Kutoyants, Estimation de paramètres pour des processus stochastiques, 1984.

D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliqué à la finance. Ellipse, 1997.

F. Lavergne and T. M. Jay, A New Strategy for Antidepressant Prescription, Frontiers in Neuroscience, vol.4, 2010.
DOI : 10.3389/fnins.2010.00192

F. Lavergne, N. Marie, and F. Mehran, Les 5 modalités de la souffrance psychique : Analyses statistiques du questionnaire des schémas (QSY-s3), 2012.

M. Ledoux, Isoperimetry and Gaussian Analysis. Ecole d'été de probabilité de Stain-Flour, 1994.

A. Lejay, Controlled differential equations as Young integrals: A simple approach, Journal of Differential Equations, vol.249, issue.8, pp.1777-1798, 2010.
DOI : 10.1016/j.jde.2010.05.006
URL : https://hal.archives-ouvertes.fr/inria-00402397

A. Lejay, Global Solutions to Rough Differential Equations with Unbounded Vector Fields, Lecture Notes in Mathematics, vol.2046, pp.215-246, 2012.
DOI : 10.1007/978-3-642-27461-9_11
URL : https://hal.archives-ouvertes.fr/inria-00451193

T. Lyons, Differential equations driven by rough signals (I): an extension of an inequality of L. C. Young, Mathematical Research Letters, vol.1, issue.4, pp.451-464, 1994.
DOI : 10.4310/MRL.1994.v1.n4.a5

T. 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, Differential Equations Driven by Rough Paths Ecole d'Eté de Probabilités de St- Flour XXXIV, Lecture Notes in Mathematics, 1908.

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

P. Malliavin and A. Thalmaier, Stochastic Calculus of Variations in Mathematical Finance, 2006.

X. Mao, A. Truman, and C. Yuan, Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching, Journal of Applied Mathematics and Stochastic Analysis, vol.44, issue.12, 2006.
DOI : 10.1137/S0363012999356325

N. Marie, Sensitivities via Rough Paths, 2011.

N. Marie, A generalized mean-reverting equation and applications, ESAIM: Probability and Statistics, vol.18, 2012.
DOI : 10.1051/ps/2014002

A. Monfort, Cours de statistique mathématique. 3e édition, 1997.

A. Neuenkirch and S. Tindel, A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise, Statistical Inference for Stochastic Processes, vol.278, issue.9, 2011.
DOI : 10.1007/s11203-013-9084-z
URL : https://hal.archives-ouvertes.fr/hal-00639030

J. Neveu, Processus aléatoires gaussiens. Presses de l, 1968.

J. Neveu, Bases mathématiques du calcul des probabilités, 1970.

I. Nourdin and A. Neuenkirch, Exact Rate of Convergence of some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion, Journal of Theoretical Probability, vol.20, issue.4, pp.871-899, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00204490

D. Nualart, The Malliavin Calculus and Related Topics, 2006.
DOI : 10.1007/978-1-4757-2437-0

J. Ouvrard, Probabilités 2, master agrégation. Collection enseignement des mathématiques, Cassini, 2004.

N. Privault and X. Wei, A Malliavin calculus approach to sensitivity analysis in insurance, Insurance: Mathematics and Economics, vol.35, issue.3, pp.679-690, 2004.
DOI : 10.1016/j.insmatheco.2004.08.003

D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 1999.

L. C. Rogers, Arbitrage with Fractional Brownian Motion, Mathematical Finance, vol.7, issue.1, pp.95-105, 1997.
DOI : 10.1111/1467-9965.00025

M. Sanz-solé and I. Torrecilla-tarantino, A Large Deviation Principle in Hölder Norm for Multiple Fractional Integrals, arXiv, 2007.

N. Simon, Pharmacocinétique de population. Collection Pharmacologie médicale, 2006.

G. Skandalis, Topologie et Analyse, 3e année, Sciences sup, 2004.

S. Stahl, Essential Psychopharmacology : Neuroscientific Basis and Applications. Second Edition, 2000.

H. J. Sussman, 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

J. Teichmann, Calculating the Greeks by cubature formulae, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2066, pp.647-670, 2006.
DOI : 10.1098/rspa.2005.1583

N. and T. Dung, Fractional geometric mean-reversion processes, Journal of Mathematical Analysis and Applications, vol.380, issue.1, pp.396-402, 2011.
DOI : 10.1016/j.jmaa.2011.03.016
URL : http://doi.org/10.1016/j.jmaa.2011.03.016

N. Towghi, Multidimensional Extension of L.C. Young's Inequality, JIPAM J. Inequal. Pure Appl. Math, vol.3, issue.13, p.pp, 2002.

F. Wu, X. Mao, and K. Chen, A highly sensitive mean-reverting process in finance and the Euler???Maruyama approximations, Journal of Mathematical Analysis and Applications, vol.348, issue.1, pp.540-554, 2008.
DOI : 10.1016/j.jmaa.2008.07.069

Y. Yamato, Stochastic differential equations and Nilpotent Lie algebras, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.1, issue.2, pp.213-242, 1979.
DOI : 10.1007/BF00535284

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

M. Zähle, Integration with Respect to Fractal Functions and Stochastic Calculus I. Probab. Theory Relat, pp.333-374, 1998.