H. Cartan, Calcul différentiel, 1967.

A. Cosso, S. Federico, F. Gozzi, M. Rosestolato, and N. Touzi, Path-dependent equations and viscosity solutions in infinite dimension, Ann. Probab, vol.46, issue.1, pp.126-174, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01117693

A. Cosso and F. Russo, Functional and Banach space stochastic calculi: path-dependent Kolmogorov equations associated with the frame of a Brownian motion, Stochastics of environmental and financial economics-Centre of Advanced Study, vol.138, pp.27-80, 2014.

A. Cosso and F. Russo, Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations, Infin. Dimens. Anal. Quantum Probab. Relat. Top, vol.19, issue.4, p.44, 2016.

C. Di-girolami and F. Russo, Infinite dimensional stochastic calculus via regularization and applications, 2010.

C. Di-girolami and F. Russo, Generalized covariation for Banach space valued processes, Itô formula and applications, Osaka Journal of Mathematics, vol.51, pp.729-783, 2014.

B. Dupire, Functional Itô calculus. Bloomberg Portfolio Research, 2009.

F. Flandoli and G. Zanco, An infinite-dimensional approach to path-dependent Kolmogorov equations, Ann. Probab, vol.44, issue.4, pp.2643-2693, 2016.
DOI : 10.1214/15-aop1031

URL : http://arxiv.org/pdf/1312.6165

H. Föllmer, C. Wu, and M. Yor, On weak Brownian motions of arbitrary order, Ann. Inst. H. Poincaré Probab. Statist, vol.36, issue.4, pp.447-487, 2000.

J. Neveu, Les Presses de l, Processus aléatoires gaussiens. Séminaire de Mathématiques Supérieures, 1968.

D. Nualart, The Malliavin calculus and related topics. Probability and its Applications
DOI : 10.1007/978-1-4757-2437-0

. Springer-verlag, , 2006.

S. Peng and F. Wang, BSDE, path-dependent PDE and nonlinear Feynman-Kac formula, Sci. China Math, vol.59, issue.1, pp.19-36, 2016.
DOI : 10.1007/s11425-015-5086-1

URL : http://arxiv.org/pdf/1108.4317

F. Russo and P. Vallois, Intégrales progressive, rétrograde et symétrique de processus non adaptés, C. R. Acad. Sci. Paris Sér. I Math, vol.312, issue.8, pp.615-618, 1991.

F. Russo and P. Vallois, Forward, backward and symmetric stochastic integration, vol.97, pp.403-421, 1993.
DOI : 10.1007/bf01195073

F. Russo and P. Vallois, Elements of stochastic calculus via regularization, Séminaire de Probabilités XL, vol.1899, pp.147-185, 2007.
DOI : 10.1007/978-3-540-71189-6_7

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