Pathwise Taylor expansions for random fields on multiple dimensional paths, Stochastic Processes and their Applications, vol.125, issue.7, 2013. ,
DOI : 10.1016/j.spa.2015.02.004
Second order PDE's in finite and infinite dimension, Lecture Notes in Mathematics, vol.1762, 2001. ,
DOI : 10.1007/b80743
Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction???diffusion equations, Journal of Evolution Equations, vol.118, issue.1, pp.83-98, 2012. ,
DOI : 10.1007/s00028-011-0124-0
Uniqueness in the dirichlet problem for some elliptic operators with discontinuous coefficients, Annali di Matematica Pura ed Applicata, vol.96, issue.no. 4, pp.161-180, 1993. ,
DOI : 10.1007/BF01759020
Representation theorem for general stochastic delay equations, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys, vol.26, pp.635-642, 1978. ,
Change of variable formulas for non-anticipative functionals on path space, Journal of Functional Analysis, vol.259, issue.4, pp.1043-1072, 2010. ,
DOI : 10.1016/j.jfa.2010.04.017
URL : https://hal.archives-ouvertes.fr/hal-00471318
A functional extension of the Ito formula, Comptes Rendus Mathematique, vol.348, issue.1-2, pp.57-61, 2010. ,
DOI : 10.1016/j.crma.2009.11.013
URL : https://hal.archives-ouvertes.fr/hal-00457533
Functional It?? calculus and stochastic integral representation of martingales, The Annals of Probability, vol.41, issue.1, pp.109-133, 2013. ,
DOI : 10.1214/11-AOP721
Kolmogorov equations for path-dependent SDEs ,
A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs, 2014. ,
On the equivalence of various weak notions of solutions of elliptic PDEs with measurable ingredients, Progress in elliptic and parabolic partial differential equations (Capri, pp.136-162, 1994. ,
Pathwise uniqueness for a class of SDE in Hilbert spaces and applications, Journal of Functional Analysis, vol.259, issue.1, pp.243-267, 2010. ,
Stochastic equations in infinite dimensions, volume 44 of Encyclopedia of Mathematics and its Applications, 1992. ,
Second order partial differential equations in Hilbert spaces, 2002. ,
DOI : 10.1017/CBO9780511543210
The covariation for Banach space valued processes and applications, Metrika, vol.77, issue.1, pp.51-104, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00780430
About Kolmogorov equations associated to window processes, preparation, 2014. ,
Infinite dimensional stochastic calculus via regularization and applications, 2010. ,
Clark-Ocone type formula for non-semimartingales with finite quadratic variation, C. R. Math. Acad. Sci. Paris, vol.349, pp.3-4209, 2011. ,
URL : https://hal.archives-ouvertes.fr/inria-00484993
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.1250007, 2012. ,
DOI : 10.1142/S0219025712500075
Generalized covariation for Banach space valued processes, Itô formula and applications, Osaka Journal of Mathematics, vol.51, issue.3, p.2014 ,
Vector integration and stochastic integration in Banach spaces, Pure and Applied Mathematics, 2000. ,
Functional It?? Calculus, SSRN Electronic Journal, 2009. ,
DOI : 10.2139/ssrn.1435551
On viscosity solutions of path dependent PDEs, The Annals of Probability, vol.42, issue.1, pp.204-236, 2014. ,
DOI : 10.1214/12-AOP788
Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I, 2013. ,
Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II, The Annals of Probability, vol.44, issue.4, 2013. ,
DOI : 10.1214/15-AOP1027
Optimal stopping under nonlinear expectation. Stochastic Process, Appl, vol.124, issue.10, pp.3277-3311, 2014. ,
DOI : 10.1016/j.spa.2014.04.006
URL : http://arxiv.org/abs/1209.6601
Kolmogorov Equation Associated to a Stochastic Navier???Stokes Equation, Journal of Functional Analysis, vol.160, issue.1, pp.312-336, 1998. ,
DOI : 10.1006/jfan.1998.3321
An infinite-dimensional approach to path-dependent Kolmogorov's equations, 2013. ,
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
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
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
Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales, Electronic Journal of Probability, vol.8, issue.0, p.pp, 2003. ,
DOI : 10.1214/EJP.v8-166
URL : https://hal.archives-ouvertes.fr/hal-00091322
Uniformly Elliptic PDEs with Bounded, Measurable Coefficients, Journal of Fourier Analysis and Applications, vol.2, issue.3, pp.237-259, 1996. ,
DOI : 10.1007/s00041-001-4031-6
Good and viscosity solutions of fully nonlinear elliptic equations, Proc. Amer, pp.533-542, 2002. ,
Diffusion equations in duals of nuclear spaces, Stochastics An International Journal of Probability and Stochastic Processes, vol.29, issue.2, pp.285-329, 1990. ,
DOI : 10.1080/17442509008833618
Weak functional Itô calculus and applications, 2014. ,
Stochastic Optimal Control Problems and Parabolic Equations in Banach Spaces, SIAM Journal on Control and Optimization, vol.47, issue.1, pp.251-300, 2008. ,
DOI : 10.1137/050632725
Semimartingales: a course on stochastic processes, De Gruyter Studies in Mathematics, vol.2, 1982. ,
DOI : 10.1515/9783110845563
Stochastic integration, 1980. ,
Stochastic functional differential equations, Research Notes in Mathematics, vol.99, 1984. ,
Note on viscosity solution of path-dependent PDE and G-martingales, 2012. ,
An Overview of Viscosity Solutions of Path-Dependent PDEs, 2014. ,
DOI : 10.1007/978-3-319-11292-3_15
URL : https://hal.archives-ouvertes.fr/hal-01057300
A new approach to Kolmogorov equations in infinite dimensions and applications to the stochastic 2D Navier???Stokes equation, Comptes Rendus Mathematique, vol.345, issue.5, pp.289-292, 2007. ,
DOI : 10.1016/j.crma.2007.07.009
Intégrales progressive, rétrograde et symétrique de processus non adaptés, C. R. Acad. Sci. Paris Sér. I Math, issue.8, pp.312615-618, 1991. ,
Forward, backward and symmetric stochastic integration. Probab. Theory Related Fields, pp.403-421, 1993. ,
DOI : 10.1007/bf01195073
The generalized covariation process and Itô formula. Stochastic Process, Appl, vol.59, issue.1, pp.81-104, 1995. ,
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
Elements of Stochastic Calculus via Regularization, Séminaire de Probabilités XL, pp.147-185, 2007. ,
DOI : 10.1007/978-3-540-71189-6_7
Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations, Discrete and Continuous Dynamical Systems, vol.35, issue.11, 2013. ,
DOI : 10.3934/dcds.2015.35.5521
Stochastic integration in UMD Banach spaces, The Annals of Probability, vol.35, issue.4, pp.1438-1478, 2007. ,
DOI : 10.1214/009117906000001006
An introduction to stochastic partial differential equations, Lecture Notes in Math, vol.1180, pp.265-439 ,
DOI : 10.1007/BFb0074920