N. U. Ahmed, Optimal control of ???-dimensional stochastic systems via generalized, Discussiones Mathematicae. Differential Inclusions, Control and Optimization, vol.21, issue.1, pp.97-126, 2001.
DOI : 10.7151/dmdico.1019

N. U. Ahmed, Generalized solutions of HJB equations applied to stochastic control on Hilbert space, Nonlinear Analysis: Theory, Methods & Applications, vol.54, issue.3, pp.495-523, 2003.
DOI : 10.1016/S0362-546X(03)00109-3

V. Barbu and G. Da-prato, A note on a Hamilton-Jacobi equation in Hilbert space, Nonlinear Analysis: Theory, Methods & Applications, vol.9, issue.12, 1983.
DOI : 10.1016/0362-546X(85)90094-X

A. Bensoussan, G. Da-prato, M. C. Delfour, and S. K. Mitter, Representation and control of infinite dimensional systems. Systems & Control: Foundations & Applications, Birkhäuser Boston Inc, 2007.

S. Cerrai, Optimal Control Problems for Stochastic Reaction-Diffusion Systems with Non-Lipschitz Coefficients, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1779-1816, 2001.
DOI : 10.1137/S0363012999356465

S. Cerrai, Stationary Hamilton--Jacobi Equations in Hilbert Spaces and Applications to a Stochastic Optimal Control Problem, SIAM Journal on Control and Optimization, vol.40, issue.3, pp.824-852, 2001.
DOI : 10.1137/S0363012999359949

P. L. Chow and J. L. Menaldi, Infinite-dimensional Hamilton-Jacobi-Bellman equations in gauss-sobolev spaces, Nonlinear Analysis: Theory, Methods & Applications, vol.29, issue.4, pp.415-426, 1997.
DOI : 10.1016/S0362-546X(96)00043-0

F. Coquet, A. Jakubowski, J. Mémin, and L. S?omi?ski, 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

G. Da-prato, A. Jentzen, and M. Röckner, A mild Itô formula for SPDEs, Preprint Arxiv, 2011.

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

G. Da-prato and J. Zabczyk, Ergodicity for infinite-dimensional systems, 1996.
DOI : 10.1017/CBO9780511662829

R. C. Dalang and L. Quer-sardanyons, Stochastic integrals for spde???s: A comparison, Expositiones Mathematicae, vol.29, issue.1, pp.67-109, 2011.
DOI : 10.1016/j.exmath.2010.09.005

A. Debussche, M. Fuhrman, and G. Tessitore, Optimal control of a stochastic heat equation with boundary-noise and boundary-control, ESAIM: Control, Optimisation and Calculus of Variations, vol.13, issue.1, pp.178-205, 2007.
DOI : 10.1051/cocv:2007001

URL : https://hal.archives-ouvertes.fr/hal-00383272

L. Denis, Solutions of stochastic partial differential equations considered as Dirichlet processes, Bernoulli, vol.10, issue.5, pp.783-827, 2004.

D. Girolami and F. Russo, Infinite dimensional stochastic calculus via regularization, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00473947

D. Girolami and F. Russo, Clark???Ocone type formula for non-semimartingales with finite quadratic variation, Comptes Rendus Mathematique, vol.349, issue.3-4, pp.3-4209, 2011.
DOI : 10.1016/j.crma.2010.11.032

URL : https://hal.archives-ouvertes.fr/inria-00484993

D. Girolami and F. Russo, GENERALIZED COVARIATION AND EXTENDED FUKUSHIMA DECOMPOSITION FOR BANACH SPACE-VALUED PROCESSES: APPLICATIONS TO WINDOWS OF DIRICHLET PROCESSES, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.15, issue.02, p.2012
DOI : 10.1142/S0219025712500075

D. Girolami and F. Russo, Generalized covariation for Banach space valued processes and Itô formula, Osaka journal of mathematics, vol.51, issue.3, p.2014

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

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

K. Du and Q. Meng, Maximum principle for infinite dimensional stochastic control systems

K. Du and Q. Meng, A Maximum Principle for Optimal Control of Stochastic Evolution Equations, SIAM Journal on Control and Optimization, vol.51, issue.6, pp.4343-4362, 2013.
DOI : 10.1137/120882433

N. Dunford, J. T. Schwartz, R. G. Bade, and . Bartle, Linear Operators. I. General Theory. With the assistance of W, Pure and Applied Mathematics, vol.7, 1958.

N. Dunford, J. T. Schwartz-william, G. Bade, and R. G. Bartle, Linear operators. Part I. Wiley Classics Library General theory, 1988.

M. Errami and F. Russo, n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes. Stochastic Process, Appl, vol.104, issue.2, pp.259-299, 2003.

W. H. Fleming and R. W. , Deterministic and stochastic optimal control, Applications of Mathematics, issue.1, 1975.
DOI : 10.1007/978-1-4612-6380-7

H. Föllmer, Dirichlet processes, Stochastic integrals (Proc. Sympos, pp.476-478, 1980.
DOI : 10.1007/BFb0088738

M. Fuhrman, Y. Hu, and G. Tessitore, Stochastic maximum principle for optimal control of spdes (extended version) Preprint

M. Fuhrman, Y. Hu, and G. Tessitore, STOCHASTIC CONTROL AND BSDES WITH QUADRATIC GROWTH, Control Theory and Related Topics, pp.80-86, 2007.
DOI : 10.1142/9789812790552_0007

URL : https://hal.archives-ouvertes.fr/hal-00368114

M. Fuhrman, Y. Hu, and G. Tessitore, Stochastic maximum principle for optimal control of spdes, Comptes Rendus Mathematique, vol.350, pp.13-14683, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00783615

M. Fuhrman, F. Masiero, and G. Tessitore, Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton???Jacobi???Bellman Equations, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4624-4651, 2010.
DOI : 10.1137/080730354

M. Fuhrman and G. Tessitore, Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control, The Annals of Probability, vol.30, issue.3, pp.1397-1465, 2002.
DOI : 10.1214/aop/1029867132

M. Fuhrman and G. Tessitore, Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces, Ann. Probab, vol.32, issue.1B, pp.607-660, 2004.

L. Gawarecki and V. Mandrekar, Stochastic differential equations in infinite dimensions with applications to stochastic partial differential equations. Probability and its Applications, 2011.

B. Goldys and F. Gozzi, Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control

F. Gozzi, Global Regular Solutions of Second Order Hamilton???Jacobi Equations in Hilbert Spaces with Locally Lipschitz Nonlinearities, Journal of Mathematical Analysis and Applications, vol.198, issue.2, pp.399-443, 1996.
DOI : 10.1006/jmaa.1996.0090

F. Gozzi, C. Marinelli, and S. Savin, On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with??Memory Effects, Journal of Optimization Theory and Applications, vol.21, issue.3, pp.291-321, 2009.
DOI : 10.1007/s10957-009-9524-5

F. Gozzi and E. Rouy, Regular Solutions of Second-Order Stationary Hamilton???Jacobi Equations, Journal of Differential Equations, vol.130, issue.1, 1996.
DOI : 10.1006/jdeq.1996.0139

URL : https://hal.archives-ouvertes.fr/inria-00074041

F. Gozzi and F. Russo, Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition. Stochastic Process, Appl, vol.116, issue.11, pp.1530-1562, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00022840

F. Gozzi and F. Russo, Weak Dirichlet processes with a stochastic control perspective. Stochastic Process, Appl, vol.116, issue.11, pp.1563-1583, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00022839

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1988.

N. V. Krylov and B. L. Rozovskii, Stochastic Evolution Equations, Stochastic differential equations: theory and applications, pp.1-70, 2007.
DOI : 10.1142/9789812770639_0001

J. A. Leon, Stochastic Fubini theorem for semimartingales in Hilbert space, Journal canadien de math??matiques, vol.42, issue.5, pp.890-901, 1990.
DOI : 10.4153/CJM-1990-046-8

P. L. Lions, Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and application, Communications in Partial Differential Equations, vol.9, issue.10, pp.1101-1174, 1983.
DOI : 10.1080/03605308308820297

P. L. Lions, Optimal control of diffusion processes and hamilton???jacobi???bellman equations part 2 : viscosity solutions and uniqueness, Communications in Partial Differential Equations, vol.25, issue.11, pp.1229-1276, 1983.
DOI : 10.1080/03605308308820301

P. L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. III. Regularity of the optimal cost function In Nonlinear partial differential equations and their applications Collège de France seminar, Res. Notes in Math, vol.93, pp.95-205, 1981.

Z. M. Ma and M. Röckner, Introduction to the theory of (nonsymmetric) Dirichlet forms. Universitext, 1992.

M. Métivier, Semimartingales: a course on stochastic processes, De Gruyter Studies in Mathematics, vol.2, 1982.
DOI : 10.1515/9783110845563

M. Métivier and J. Pellaumail, Stochastic integration. Probability and Mathematical Statistics, 1980.

P. A. Meyer, Notes sur les integrales stochastiques. I Integrales hilbertiennes, Séminaire de Probabilites XI, pp.446-481, 1977.
DOI : 10.1007/BF00539856

R. Mikulevicius and B. Rozovskii, Martingale problems for stochastic PDE???s, Stochastic partial differential equations: six perspectives, pp.243-326, 1999.
DOI : 10.1090/surv/064/06

B. Oksendal, A. Sulem, and T. Zhang, Singular control of spdes and backward spdes with reflection
URL : https://hal.archives-ouvertes.fr/hal-00639550

M. Ondreját, Uniqueness for stochastic evolution equations in Banach spaces, Dissertationes Mathematicae, vol.426, p.63, 2004.
DOI : 10.4064/dm426-0-1

C. Prévôt and M. Röckner, A concise course on stochastic partial differential equations, Lecture Notes in Mathematics, 1905.

M. C. Quenez, Stochastic control and BSDEs, Backward stochastic differential equations, pp.83-99, 2007.

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, Noncausal stochastic integration for làd làg processes In Stochastic analysis and related topics, Stochastics Monogr, vol.8, pp.227-263, 1992.

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

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

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

A. ?wi¸ech?wi¸ech, Unbounded " second order partial differential equations in infinite-dimensional Hilbert spaces, Comm. Partial Differential Equations, vol.19, pp.11-121999, 1994.

J. B. Walsh, An introduction to stochastic partial differential equations, Lecture Notes in Math, vol.1180, pp.265-439, 1986.
DOI : 10.1007/BFb0074920

J. Yong and X. Y. Zhou, Stochastic controls, Hamiltonian systems and HJB equations, Applications of Mathematics, vol.43, 1999.