S. Albeverio and B. Rüdiger, Stochastic Integrals and the L??vy-Ito Decomposition Theorem on Separable Banach Spaces, Stochastic Analysis and Applications, vol.23, issue.2, pp.217-253, 2005.
DOI : 10.1081/SAP-200026429

D. Charalambos, K. C. Aliprantis, and . Border, Infinite dimensional analysis, 2006.

C. Bender, T. Sottinen, and E. Valkeila, Pricing by hedging and no-arbitrage beyond??semimartingales, Finance and Stochastics, vol.2, issue.2, pp.441-468, 2008.
DOI : 10.1007/s00780-008-0074-8

J. Bertoin, Les processus de dirichlet et tant qu'espace de banach, Stochastics, vol.851, issue.2, pp.155-168, 1986.
DOI : 10.1080/17442508608833406

F. Biagini and B. Øksendal, A General Stochastic Calculus Approach to Insider Trading, Applied Mathematics and Optimization, vol.52, issue.2, pp.167-181, 2005.
DOI : 10.1007/s00245-005-0825-2

H. Brezis, Analyse fonctionnelle Collection Mathématiques Appliquées pour la Ma??triseMa??trise. [Collection of Applied Mathematics for the Master's Degree], Théorie et applications. [Theory and applications], 1983.

B. Zdziss, Stochastic partial differential equations in M-type 2 Banach spaces. Potential Anal, pp.1-45, 1995.

H. Cartan, Calcul différentiel, 1967.

A. Chojnowska and M. , Representation theorem for general stochastic delay equations

F. Coquet, A. Jakubowski, J. Mémin, S. Leszek, and . Lomi´nskilomi´nski, Natural Decomposition of Processes and Weak Dirichlet Processes, memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX, pp.81-116, 2006.
DOI : 10.1007/978-3-540-35513-7_8

URL : https://hal.archives-ouvertes.fr/hal-00001360

R. Coviello and F. Russo, Modeling financial assets without semimartingales, 2006.
DOI : 10.1016/j.bulsci.2011.06.008

URL : http://arxiv.org/abs/1102.2050

R. Coviello and F. Russo, Nonsemimartingales: Stochastic differential equations and weak Dirichlet processes, The Annals of Probability, vol.35, issue.1, pp.255-308, 2007.
DOI : 10.1214/009117906000000566

URL : https://hal.archives-ouvertes.fr/hal-00020068

G. Da, P. , and J. Zabczyk, Stochastic equations in infinite dimensions, volume 44 of Encyclopedia of Mathematics and its Applications, 1992.

C. Robert and . Dalang, Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s. Electron, J. Probab, vol.4, issue.29, p.pp, 1999.

E. Dettweiler, On the martingale problem for Banach space valued stochastic differential equations, Journal of Theoretical Probability, vol.85, issue.2
DOI : 10.1007/BF01053408

E. Dettweiler, Stochastic integration relative to Brownian motion on a general Banach space, Do? ga Mat, vol.15, issue.2, pp.58-97, 1991.

G. Di-nunno, T. Meyer-brandis, B. Øksendal, and F. Proske, MALLIAVIN CALCULUS AND ANTICIPATIVE IT?? FORMULAE FOR L??VY PROCESSES, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.08, issue.02, pp.235-258, 2005.
DOI : 10.1142/S0219025705001950

J. Diestel, J. J. Uhl, and R. I. , Vector measures, J. Pettis, Mathematical Surveys, issue.15, 1977.

N. Dinculeanu, Vector integration and stochastic integration in Banach spaces, Pure and Applied Mathematics, 2000.

N. Dunford and J. T. Schwartz, Linear operators. Part I. Wiley Classics Library, 1988.

. Bartle, Reprint of the 1958 original

N. Dunford, J. T. Schwartz-william, G. Bade, and R. G. Bartle, Linear operators. Part II Wiley Classics Library Spectral theory. Selfadjoint operators in Hilbert space, 1988.

N. Dunford and J. T. Schwartz, Linear operators. Part III. Wiley Classics Library, 1988.

R. G. Bartle, Reprint of the 1971 original

M. Errami and F. Russo, Covariation de convolution de martingales, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.5
DOI : 10.1016/S0764-4442(98)85014-3

M. Errami and F. Russo, n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes, Stochastic Processes and their Applications, vol.104, issue.2, pp.259-299, 2003.
DOI : 10.1016/S0304-4149(02)00238-7

K. Es-sebaiy and C. A. Tudor, MULTIDIMENSIONAL BIFRACTIONAL BROWNIAN MOTION: IT?? AND TANAKA FORMULAS, Stochastics and Dynamics, vol.07, issue.03, pp.365-388, 2007.
DOI : 10.1142/S0219493707002050

F. Flandoli and F. Russo, Generalized Integration and Stochastic ODEs, The Annals of Probability, vol.30, issue.1, pp.270-292, 2002.
DOI : 10.1214/aop/1020107768

F. Flandoli, F. Russo, and J. Wolf, Some SDEs with distributional drift. I. General calculus, Osaka J. Math, vol.40, issue.2, pp.493-542, 2003.
DOI : 10.1515/156939704323074700

H. Föllmer, C. Wu, and M. Yor, On weak Brownian motions of arbitrary order

M. Fuhrman and G. Tessitore, Backward stochastic differential equations in finite and infinite dimensions. Lecture notes: Politecnico di Milano, 2004.

I. M. Gelfand and N. Ya, Applications of harmonic analysis, Vilenkin. Generalized functions, vol.4, 1964.

F. Gozzi and F. Russo, Verification theorems for stochastic optimal control problems via a time dependent Fukushima???Dirichlet decomposition, Stochastic Processes and their Applications, pp.1530-1562, 2006.
DOI : 10.1016/j.spa.2006.04.008

URL : https://hal.archives-ouvertes.fr/hal-00022840

F. Gozzi and F. Russo, Weak Dirichlet processes with a stochastic control perspective, Stochastic Processes and their Applications, pp.1563-1583, 2006.
DOI : 10.1016/j.spa.2006.04.009

URL : https://hal.archives-ouvertes.fr/hal-00022839

I. Nourdin, F. Russo, M. Gradinaru, and P. Vallois, m-order integrals and generalized itô's formula: the case of factional brownian motion with any hurst index, pp.2003-2010

M. Russo-francesco-gradinaru and P. Vallois, Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index

M. Hinz and M. Zähle, Gradient-type noises I???partial and hybrid integrals, Complex Variables and Elliptic Equations, vol.27, issue.6
DOI : 10.1137/1010093

C. Houdré and J. Villa, An example of infinite dimensional quasi-helix, Stochastic models, pp.195-201, 2002.
DOI : 10.1090/conm/336/06034

K. Itô, Differential equations determining Markov processes, Zenkoku Shijo Sugaku Danwakai, vol.1077, pp.1352-400, 1942.

J. Jacod, Calcul stochastique etprobì emes de martingales, Lecture Notes in Mathematics, vol.714, 1979.

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, 2003.
DOI : 10.1007/978-3-662-02514-7

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1991.

A. Kohatsu-higa and A. Sulem, UTILITY MAXIMIZATION IN AN INSIDER INFLUENCED MARKET, Mathematical Finance, vol.70, issue.1, pp.153-179, 2006.
DOI : 10.1016/0304-4149(95)93237-A

URL : https://hal.archives-ouvertes.fr/inria-00070624

I. Kruk, F. Russo, and C. A. Tudor, Wiener integrals, Malliavin calculus and covariance measure structure, Journal of Functional Analysis, vol.249, issue.1, pp.92-142, 2007.
DOI : 10.1016/j.jfa.2007.03.031

URL : https://hal.archives-ouvertes.fr/hal-00078163

P. Lei and D. Nualart, A decomposition of the bifractional Brownian motion and some applications, Statistics & Probability Letters, vol.79, issue.5, pp.619-624, 2009.
DOI : 10.1016/j.spl.2008.10.009

J. A. León, R. Navarro, and D. Nualart, An Anticipating Calculus Approach to the Utility Maximization of an Insider, Conference on Applications of Malliavin Calculus in Finance (Rocquencourt, pp.171-185, 2001.
DOI : 10.1111/1467-9965.00012

M. Métivier and J. Pellaumail, Stochastic integration, 1980.

J. Neveu, Processus aléatoires gaussiens

D. Nualart, The Malliavin calculus and related topics. Probability and its Applications

B. Øksendal and T. Zhang, The Itô-Ventzell formula and forward stochastic differential equations driven by Poisson random measures, Osaka J. Math, vol.4450, issue.1, pp.207-230, 2007.

E. Pardoux, Sur deséquationsdeséquations aux dérivées partielles stochastiques monotones, C. R. Acad. Sci

E. Pardoux and . Exp, ´ Equations aux dérivées partielles stochastiques de type monotoneColì ege de France, Séminaire sur lesÉquationsles´lesÉquations aux Dérivées Partielles III BIBLIOGRAPHY 185 [52] ´ Etienne Pardoux. Equations aux dérivées partielles stochastiques non linéaires monotones. Etude de solutions fortes de type Ito, 1974.

E. Philip and . Protter, Stochastic integration and differential equations, Applications of Mathematics, vol.21, 2004.

D. Revuz and M. Yor, Continuous martingales and Brownian motion, 1999.

M. Röckner and C. Prévôt, A Concise Course on Stochastic Partial Differential Equations, Lecture Notes in Mathematics, 1905.

F. Russo and C. A. Tudor, On bifractional Brownian motion, Stochastic Processes and their Applications, pp.830-856, 2006.
DOI : 10.1016/j.spa.2005.11.013

URL : https://hal.archives-ouvertes.fr/hal-00130627

F. Russo and P. Vallois, Intégrales progressive, rétrograde et symétrique de processus non adaptés, C. R. Acad. Sci. Paris Sér. I Math, issue.8, pp.312615-618, 1991.

F. Russo and P. Vallois, Forward, backward and symmetric stochastic integration. Probab. Theory Related Fields, pp.403-421, 1993.

F. Russo and P. Vallois, The generalized covariation process and Itô formula. Stochastic Process, Appl, vol.59, issue.1, pp.81-104, 1995.

F. Russo and P. Vallois, Stochastic calculus with respect to continuous finite quadratic variation processes, Stochastics An International Journal of Probability and Stochastic Processes, vol.70, issue.1, pp.1-40, 2000.
DOI : 10.1080/17442500008834244

F. Russo and P. Vallois, Elements of Stochastic Calculus via Regularization, Séminaire de Probabilités XL, pp.147-185, 2007.
DOI : 10.1007/978-3-540-71189-6_7

F. Russo, P. Vallois, and J. Wolf, A Generalized Class of Lyons-Zheng Processes, Bernoulli, vol.7, issue.2, pp.363-379, 2001.
DOI : 10.2307/3318744

R. A. Ryan, Introduction to tensor products of Banach spaces, 2002.
DOI : 10.1007/978-1-4471-3903-4

G. M. John, P. E. Schoenmakers, and . Kloeden, Robust option replication for a Black-Scholes model extended with nondeterministic trends, J. Appl. Math. Stochastic Anal, vol.12, issue.2, pp.113-120, 1999.

W. Stannat, The theory of generalized Dirichlet forms and its applications in analysis and stochastics, Memoirs of the American Mathematical Society, vol.142, issue.678, p.101, 1999.
DOI : 10.1090/memo/0678

M. Elias and . Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, issue.30, 1970.

F. Trèves, Topological vector spaces, distributions and kernels, 68] A. S. ¨ Ustünel. Representation of the distributions on Wiener space and stochastic calculus of variations, 1967.

J. Van-neerven and M. Riedle, A Semigroup Approach to Stochastic Delay Equations in Spaces of Continuous Functions, Semigroup Forum, vol.74, issue.2, pp.227-239, 2007.
DOI : 10.1007/s00233-005-0649-7

J. B. Walsh, An introduction to stochastic partial differential equations InÉcoleIn´InÉcole d'´ eté de probabilités de Saint-Flour, XIV?1984, Lecture Notes in Math, vol.1180, 1986.

. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, volume 73 of Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 1984.

F. Yan and S. Mohammed, A Stochastic Calculus for Systems with Memory, Stochastic Analysis and Applications, vol.23, issue.3, pp.613-657, 2005.
DOI : 10.1007/BF00339940

Y. K¯, Functional analysis Classics in Mathematics, 1980.

M. Zähle, Integration with respect to fractal functions and stochastic calculus, II. Math. Nachr, vol.225, pp.145-183, 2001.