V. Bally, The central limit theorem for a nonlinear algorithm based on quantization, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci, vol.460, pp.221-241, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00693136

B. Bergé, I. D. Chueshov, and &. , Vuillermot -On the behavior of solutions to certain parabolic SPDE's driven by Wiener processes, Stochastic Process. Appl, vol.92, issue.2, pp.237-263, 2001.

R. Belfadli and K. , Es-Sebaiy & Y. Ouknine -Parameter estimation for fractional ornstein-uhlenbeck processes : non-ergodic case, 2011.

F. Baudoin, Hairer -A version of Hörmander's theorem for the fractional Brownian motion, Probab. Theory Related Fields, vol.139, issue.3-4, pp.373-395, 2007.

G. Barles-&-e.-lesigne--sde, . Bsde, and . Pde, Backward stochastic differential equations, vol.364, pp.47-80, 1995.

V. Bally and &. Matoussi, Weak solutions for SPDEs and backward doubly stochastic differential equations, J. Theoret. Probab, vol.14, issue.1, pp.125-164, 2001.

R. Buckdahn and &. J. Ma, Stochastic viscosity solutions for nonlinear stochastic partial differential equations. I., Stochastic Process, Appl, vol.93, issue.2, pp.181-204, 2001.

V. Bally, Pagès -Error analysis of the optimal quantization algorithm for obstacle problems, Stochastic Process. Appl, vol.106, issue.1, pp.1-40, 2003.

, A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems, Bernoulli, vol.9, issue.6, pp.1003-1049, 2003.

V. Bally, G. Pagès, and &. , Monte Carlo and probabilistic methods for partial differential equations, Monte Carlo Methods Appl, vol.7, issue.1-2, pp.21-33, 2000.

V. Bally, G. Pagès, and &. , Printems -First-order schemes in the numerical quantization method, Conference on Applications of Malliavin Calculus in Finance, vol.13, pp.1-16, 2001.

H. Brezis, Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise, 1983.

V. Bally, Saussereau -Approximation of the Snell envelope and American options prices in dimension one, ESAIM Probab. Statist, vol.6, pp.1-19, 2002.

A. , Borodin & P. Salminen -Handbook of Brownian motion-facts and formulae, second éd, Probability and its Applications, 2002.

V. Bally, Saussereau -A relative compactness criterion in Wiener-Sobolev spaces and application to semi-linear stochastic PDEs, J. Funct. Anal, vol.210, issue.2, pp.465-515, 2004.

B. Bergé, &. Saussereau, and -. , On the long-time behaviour of a class of parabolic SPDE's : monotonicity methods and exchange of stability, ESAIM Probab. Stat, vol.9, pp.254-276, 2005.

C. Bauzet, G. Vallet, and &. Wittbold, The cauchy problem for a conservation law with a multiplicative stochastic perturbation, Journal of Hyperbolic Differential Equations, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00868326

T. Cass-&-p, Friz -Densities for rough differential equations under Hörmander's condition, Ann. of Math, issue.2, pp.2115-2141, 2010.

T. Cass, P. Friz, and &. , Victoir -Non-degeneracy of Wiener functionals arising from rough differential equations, Trans. Amer. Math. Soc, vol.361, issue.6, pp.3359-3371, 2009.

I. Chueshov, Monotone random systems theory and applications, vol.1779, 2002.

L. Coutin, Qian -Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields, vol.122, issue.1, pp.108-140, 2002.

A. Chronopoulo and &. S. Tindel, On inference for fractional differential equations, 2011.

I. D. Chueshov-&-p, Vuillermot -Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise : Stratonovitch's case, Probab. Theory Related Fields, vol.112, issue.2, pp.149-202, 1998.

, Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise : Itô's case, Stochastic Anal. Appl, vol.18, issue.4, pp.581-615, 2000.

C. M. , Dafermos -Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J, vol.26, issue.6, pp.1097-1119, 1977.

C. M. , Dafermos -Hyperbolic conservation laws in continuum physics, second éd, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, vol.325, 2005.

L. Decreusefond, Stochastic integration with respect to Volterra processes, Ann. Inst. H. Poincaré Probab. Statist, vol.41, issue.2, pp.123-149, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00358143

H. Djellout, A. Guillin, and &. Wu, Transportation cost-information inequalities and applications to random dynamical systems and diffusions, Ann. Probab, vol.32, issue.3B, pp.2702-2732, 2004.

M. Dozzi and J. A. , López-Mimbela -Finite-time blowup and existence of global positive solutions of a semi-linear SPDE, Stochastic Process. Appl, vol.120, issue.6, pp.767-776, 2010.

, Darses & I. Nourdin -Dynamical properties and characterization of gradient drift diffusion, Electron. Comm. Probab, vol.12, pp.390-400, 2007.

, Stochastic derivatives for fractional diffusions, Ann. Probab, vol.35, issue.5, pp.1998-2020, 2007.

S. Darses, I. Nourdin, and &. , Peccati -Differentiating ?-fields for Gaussian and shifted Gaussian processes, Stochastics, vol.81, issue.1, pp.79-97, 2009.

H. Doss, Liens entre équations différentielles stochastiques et ordinaires, vol.13, pp.99-125, 1977.

G. Da-prato, P. Malliavin, and &. , Nualart -Compact families of Wiener functionals, C. R. Acad. Sci. Paris Sér. I Math, vol.315, issue.12, pp.1287-1291, 1992.

S. Darses, Saussereau -Time reversal for drifted fractional Brownian motion with Hurst index H > 1/2, Electron, J. Probab, vol.12, issue.43, pp.1181-1211, 2007.

Y. , Saussereau -Quelle problématique pour un enseignement des probabilités en troisième ?, Repères IREM, p.77, 2009.

, La prise de décision de la seconde à la première, Repères IREM, vol.85, 2011.

A. Debussche and &. Vovelle, Scalar conservation laws with stochastic forcing, J. Funct. Anal, vol.259, issue.4, pp.1014-1042, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00451641

W. E. , K. Khanin, and A. , Sinai -Invariant measures for Burgers equation with stochastic forcing, Ann. of Math, issue.2, pp.877-960, 2000.

L. C. , Evans -Partial differential equations, Graduate Studies in Mathematics, vol.19, 1998.

X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, vol.480, pp.1-96, 1975.

J. Feng, Nualart -Stochastic scalar conservation laws, J. Funct. Anal, vol.255, issue.2, pp.313-373, 2008.

H. , Föllmer -Time reversal on Wiener space, Stochastic processes-mathematics and physics, vol.1158, pp.119-129, 1984.

W. H. Fleming and H. M. , Soner -Controlled Markov processes and viscosity solutions, Applications of Mathematics, vol.25, 1993.

M. J. Garrido-atienza and P. E. Kloeden, Neuenkirch -Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion, Appl. Math. Optim, vol.60, issue.2, pp.151-172, 2009.

E. Gobet, G. Pagès, H. Pham, and &. , Printems -Discretization and simulation of the Zakai equation, SIAM J. Numer. Anal, vol.44, issue.6, pp.2505-2538, 2006.

A. M. Garsia, E. Rodemich, and &. Rumsey, A real variable lemma and the continuity of paths of some Gaussian processes, Indiana Univ. Math. J, vol.20, pp.565-578, 1970.

Y. Hu-&-d, Nualart -Differential equations driven by Hölder continuous functions of order greater than 1/2, in Stochastic analysis and applications, Abel Symp, vol.2, pp.399-413, 2007.

, Parameter estimation for fractional Ornstein-Uhlenbeck processes, Statist. Probab. Lett, vol.80, issue.11, pp.1030-1038, 2010.

Y. Hu, D. Nualart, and &. , Song -Fractional martingales and characterization of the fractional Brownian motion, Ann. Probab, vol.37, issue.6, pp.2404-2430, 2009.

L. Hörmander, Lectures on nonlinear hyperbolic differential equations, Mathéma-tiques & Applications (Berlin) [Mathematics & Applications], vol.26, 1997.

U. , Haussmann & É. Pardoux -Time reversal of diffusions, Ann. Probab, vol.14, issue.4, pp.1188-1205, 1986.

M. S. Hairer-&-n, Pillai -Ergodicity of hypoelliptic SDEs driven by a fractional Brownian motion, Ann. Inst. Henri Poincaré Probab. Stat, vol.47, issue.2, pp.601-628, 2011.

G. Hetzer, W. Shen, and &. S. Zhu, Asymptotic behavior of positive solutions of random and stochastic parabolic equations of Fisher and Kolmogorov types, J. Dynam. Differential Equations, vol.14, issue.1, pp.139-188, 2002.

M. L. Kleptsyna and &. Breton, Statistical analysis of the fractional OrnsteinUhlenbeck type process, Stat. Inference Stoch. Process, vol.5, issue.3, pp.229-248, 2002.

S. , Kru?kov -First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), vol.81, issue.123, pp.228-255, 1970.

S. Kusuoka, Stroock -Applications of the Malliavin calculus, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.II, issue.1, pp.1-76, 1985.

S. Kusuoka, The nonlinear transformation of Gaussian measure on Banach space and absolute continuity. I, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.29, issue.3, pp.567-597, 1982.

D. , Lamberton -Error estimates for the binomial approximation of American put options, Ann. Appl. Probab, vol.8, issue.1, pp.206-233, 1998.

D. , Lamberton -Brownian optimal stopping and random walks, Appl. Math. Optim, vol.45, issue.3, pp.283-324, 2002.

M. Ledoux, The concentration of measure phenomenon, Mathematical Surveys and Monographs, vol.89, 2001.

X. J. Li-&-t, Lyons -Smoothness of Itô maps and diffusion processes on path spaces. I, Ann. Sci. École Norm. Sup, issue.4, pp.649-677, 2006.

S. Lototsky and R. &. Mikulevicius, Rozovskii -Nonlinear filtering revisited : a spectral approach, SIAM J. Control Optim, vol.35, issue.2, pp.435-461, 1997.

S. V. , Lototsky -Wiener chaos and nonlinear filtering, Appl. Math. Optim, vol.54, issue.3, pp.265-291, 2006.

D. Lamberton-&-g, Pagès -Sur l'approximation des réduites, Ann. Inst. H. Poincaré Probab. Statist, vol.26, issue.2, pp.331-355, 1990.

T. Lyons-&-z.-qian, System control and rough paths, Oxford Mathematical Monographs, 2002.

D. C. Lamberton-&-l, Rogers -Optimal stopping and embedding, J. Appl. Probab, vol.37, issue.4, pp.1143-1148, 2000.

T. Lyons, Differential equations driven by rough signals. I. An extension of an inequality of L. C. Young, Math. Res. Lett, vol.1, issue.4, pp.451-464, 1994.

R. Manthey-&-k.-mittmann, On a class of stochastic functional-differential equations arising in population dynamics, Stochastics Stochastics Rep, vol.64, issue.1-2, pp.75-115, 1998.

A. Millet, D. Nualart, and &. , Sanz -Integration by parts and time reversal for diffusion processes, Ann. Probab, vol.17, issue.1, pp.208-238, 1989.

M. N. Mishra-&-b, Prakasa Rao -Nonparametric estimation of trend for stochastic differential equations driven by fractional Brownian motion, Stat. Inference Stoch. Process, vol.14, issue.2, pp.101-109, 2011.

E. Nelson, Dynamical theories of Brownian motion, 1967.

D. Nualart-&-y, Ouknine -Regularization of differential equations by fractional noise, Stochastic Process. Appl, vol.102, issue.1, pp.103-116, 2002.

D. Nualart-&-a, R??canu -Differential equations driven by fractional Brownian motion, Collect. Math, vol.53, issue.1, pp.55-81, 2002.

I. Nourdin and &. T. Simon, On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion, Statist. Probab. Lett, vol.76, pp.907-912, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00083102

D. Nualart-&-b, Saussereau -Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion, Stochastic Process. Appl, vol.119, issue.2, pp.391-409, 2009.

A. Neuenkirch, Tindel -A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise, 2011.

, Nualart -The Malliavin calculus and related topics, second éd, Probability and its Applications, 2006.

O. A. , Ole?nik -Discontinuous solutions of non-linear differential equations, Uspehi Mat. Nauk (N.S.), vol.12, issue.3, pp.3-73, 1957.

B. Øksendal, G. &. Våge, and . Zhao, Asymptotic properties of the solutions to stochastic KPP equations, Proc. Roy. Soc. Edinburgh Sect. A, vol.130, issue.6, pp.1363-1381, 2000.

, Two properties of stochastic KPP equations : ergodicity and pathwise property, Nonlinearity, vol.14, issue.3, pp.639-662, 2001.

É. Pardoux, Grossissement d'une filtration et retournement du temps d'une diffusion, Lecture Notes in Math, vol.85, pp.48-55, 1984.

É. Pardoux, Filtrage non linéaire et équations aux dérivées partielles stochastiques associées, vol.1464, pp.67-163, 1991.

A. Papavasiliou, Ladroue -Parameter estimation for rough differential equations, Ann. Statist, vol.39, issue.4, pp.2047-2073, 2011.

É. G. Pardoux-&-s, Peng -Adapted solution of a backward stochastic differential equation, Systems Control Lett, vol.14, issue.1, pp.55-61, 1990.

É. G. Pardoux-&-s, Peng -Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Related Fields, vol.98, issue.2, pp.209-227, 1994.

C. Rovira, Sanz-Solé -The law of the solution to a nonlinear hyperbolic SPDE, J. Theoret. Probab, vol.9, issue.4, pp.863-901, 1996.

D. Revuz-&-m, Yor -Continuous martingales and Brownian motion, third éd, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, vol.293, 1999.

B. , Saussereau -Sur une classe d'équations aux dérivées partielles stochastiques, 2001.

, Deviation probability bounds for fractional martingales and related remarks, Statist. Probab. Lett, vol.82, pp.1610-1618, 2012.

, A new numerical scheme for stochastic partial differential equations with multiplicative noise, 2012.

, Nonparametric inference for fractional diffusion, 2012.

, A remark on the mean square distance between the solutions of fractional SDEs and Brownian SDEs, Stochastics, vol.84, issue.1, pp.1-19, 2012.

, Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion, Bernoulli, vol.18, issue.1, pp.1-23, 2012.

D. Serre, Hyperbolicity, entropies, shock waves, Translated from the 1996 French original by, Systems of conservation laws. 1, 1999.

S. G. Samko and A. A. , Kilbas & O. I. Marichev -Fractional integrals and derivatives, 1993.

R. B. , Sowers -Large deviations for a reaction-diffusion equation with non-Gaussian perturbations, Ann. Probab, vol.20, issue.1, pp.504-537, 1992.

V. G. Spokoiny, Adaptive drift estimation for nonparametric diffusion model, Ann. Statist, vol.28, issue.3, pp.815-836, 2000.

B. Saussereau-&-l, Stoica -Scalar conservation laws with fractional stochastic forcing : existence, uniqueness and invariant measure, Stochastic Process. Appl, vol.122, issue.2, pp.1456-1486, 2012.

H. J. , Sussmann -On the gap between deterministic and stochastic ordinary differential equations, Ann. Probability, vol.6, issue.1, pp.19-41, 1978.

C. A. Tudor-&-f, Viens -Statistical aspects of the fractional stochastic calculus, Ann. Statist, vol.35, issue.3, pp.1183-1212, 2007.

, Statistical aspects of the fractional stochastic calculus, 2007.

L. C. , Young -An inequality of the Hölder type connected with Stieltjes integration, Acta Math, vol.67, pp.251-282, 1936.

M. , Zähle -Integration with respect to fractal functions and stochastic calculus. I, Probab. Theory Related Fields, vol.111, pp.333-374, 1998.