A. Barrasso and F. Russo, Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. part II: Decoupled mild solutions and examples, p.1505974, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01431559

J. M. Bismut, Conjugate convex functions in optimal stochastic control, Journal of Mathematical Analysis and Applications, vol.44, issue.2, pp.384-404, 1973.
DOI : 10.1016/0022-247X(73)90066-8
URL : https://doi.org/10.1016/0022-247x(73)90066-8

E. B. Davies, Heat kernels and spectral theory, volume 92 of Cambridge Tracts in Mathematics, 1989.

F. Delarue and R. Diel, Rough paths and 1d SDE with a time dependent distributional drift: application to polymers. Probab. Theory Related Fields, pp.1-63, 2016.
DOI : 10.1007/s00440-015-0626-8
URL : https://hal.archives-ouvertes.fr/hal-00947201

J. Diehl and J. Zhang, Backward stochastic differential equations with Young drift, Probability, Uncertainty and Quantitative Risk, vol.67, issue.1, p.17, 2017.
DOI : 10.1007/BF02401743
URL : https://doi.org/10.1186/s41546-017-0016-5

H. Engelbert and J. Wolf, Strong Markov Local Dirichlet Processes and Stochastic Differential Equations, Theory of Probability & Its Applications, vol.43, issue.2, pp.331-348, 1998.
DOI : 10.1137/S0040585X97976829

M. Erraoui, Y. Ouknine, and A. Sbi, Reflected solutions of backward stochastic differential equations with distribution as terminal condition, Random Operators and Stochastic Equations, vol.6, issue.1, pp.1-16, 1998.
DOI : 10.1515/rose.1998.6.1.1

F. Flandoli, E. Issoglio, and F. Russo, Multidimensional stochastic differential equations with distributional drift, Transactions of the American Mathematical Society, vol.369, issue.3, pp.1665-1688, 2017.
DOI : 10.1090/tran/6729
URL : https://hal.archives-ouvertes.fr/hal-00935399

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

F. Flandoli, F. Russo, and J. Wolf, Some SDEs with distributional drift. - Part II: Lyons-Zheng structure, It??'s formula and semimartingale characterization, Random Operators and Stochastic Equations, vol.12, issue.2, pp.145-184, 2004.
DOI : 10.1163/156939704323074700

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

E. Issoglio, Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the Solution, Zeitschrift f??r Analysis und ihre Anwendungen, vol.32, issue.1, pp.37-53, 2013.
DOI : 10.4171/ZAA/1473

E. Issoglio and S. Jing, Forward-Backward SDEs with distributional coefficients . preprint -ArXiv, 2016.

I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, 1991.
DOI : 10.1007/978-1-4684-0302-2

A. Lunardi, ´. E. Pardoux, and S. G. Peng, Analytic semigroups and optimal regularity in parabolic problems Adapted solution of a backward stochastic differential equation, Progress in Nonlinear Differential Equations and their Applications, pp.55-61, 1990.

E. Pardoux and A. , Stochastic differential equations, backward SDEs, partial differential equations, volume 69 of Stochastic Modelling and Applied Probability
DOI : 10.1007/978-3-319-05714-9

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

T. Runst and W. Sickel, Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, volume 3 of de Gruyter Series in Nonlinear Analysis and Applications, 1996.

F. Russo and G. Trutnau, Some parabolic PDEs whose drift is an irregular random noise in space, The Annals of Probability, vol.35, issue.6, pp.2213-2262, 2007.
DOI : 10.1214/009117906000001178
URL : https://hal.archives-ouvertes.fr/hal-00019856

F. Russo and P. Vallois, The generalized covariation process and Ito formula, Stochastic Processes and their Applications, pp.81-104, 1995.
DOI : 10.1016/0304-4149(95)93237-A
URL : https://doi.org/10.1016/0304-4149(95)93237-a

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 and L. Wurzer, Elliptic PDEs with distributional drift and backward SDEs driven by a c??dl??g martingale with random terminal time, Stochastics and Dynamics, vol.21, issue.04, pp.1750030-2017
DOI : 10.1007/BF01195073