E. Abe, Cambridge Tracts in Mathematics, 2004.

Y. Bruned, A. Chandra, I. Chevyrev, and M. Hairer, Renormalising SPDEs in regularity structures, 2017.

H. Bahouri, J. Chemin, and R. Danchin, Fourier analysis and nonlinear partial differential equations, Grundlehren der Mathematischen Wissenschaften, vol.343
URL : https://hal.archives-ouvertes.fr/hal-00732127

. Springer, , 2011.

Y. Bruned, C. Curry, and K. Ebrahimi-fard, Quasishuffle algebras and renormalisation of rough differential equations, 2018.

C. Bellingeri, An Itô type formula for the additive stochastic heat equation, 2018.

C. Bellingeri, Rough change of variable formulae and quasigeometric rough paths, 2019.

C. Bellingeri, Rough Itô formulae for the stochastic heat equation

C. Bayer, P. K. Friz, P. Gassiat, J. Martin, and B. Stemper, A regularity structure for rough volatility, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01936400

Y. Bruned, F. Gabriel, M. Hairer, and L. Zambotti, Geometric stochastic heat equations. arXiv e-prints, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02013995

Y. Bruned, M. Hairer, and L. Zambotti, Algebraic renormalisation of regularity structures, Inventiones mathematicae, vol.215, issue.3, pp.1039-1156, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02090026

H. Boedihardjo, Decay rate of iterated integrals of branched rough paths, Analyse Non Linéaire, vol.35, issue.4, pp.945-969, 2018.

Y. Bruned, Singular KPZ Type Equations. Theses, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01306427

Y. Bruned, Recursive formulae in regularity structures, Stochastic Partial Differential Equations, vol.6, pp.525-564, 2018.

K. Burdzy and J. Swanson, A change of variable formula with itô correction term, Annals of Probability, vol.38, issue.5, pp.1817-1869, 2010.

J. Butcher, An algebraic theory of integration methods, Math. Comp, vol.26, pp.79-106, 1972.

J. R. Cannon, The one-dimensional heat equation, Encyclopedia of Mathematics and its Applications, vol.23, 1984.

C. Curry, K. Ebrahimi-fard, D. Manchon, and H. , Munthe-Kaas. Planarly branched rough paths and rough differential equations on homogeneous spaces. arXiv preprint 1804.08515v3, 2018.

A. Chandra and M. Hairer, An analytic BPHZ theorem for regularity structures, 2016.

A. Connes and D. Kreimer, Hopf algebras, renormalization and noncommutative geometry, Communications in Mathematical Physics, vol.199, issue.1, pp.203-242, 1998.

P. Cheridito and D. Nualart, Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H ? (0, 1/2). Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.41, pp.1049-1081, 2005.

J. Colombeau, New generalized functions and multiplication of distributions, North-Holland Mathematics Studies, vol.84, p.90, 1984.

R. Cont and N. Perkowski, Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity, Transactions of the American Mathematical Society. Series B, vol.6, pp.161-186, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01742614

, Stochastic partial differential equations: six perspectives, Mathematical Surveys and Monographs, vol.64, 1999.

R. Cairoli and J. B. Walsh, Stochastic integrals in the plane, Acta Mathematica, vol.134, pp.111-183, 1975.

G. Da and P. , On perturbations of symmetric gaussian diffusions, Stochastic Analysis and Applications, vol.17, issue.3, pp.369-381, 1999.

G. Da-prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications, 2014.

K. Ebrahimi-fard, J. A. Simon, F. Malham, A. Patras, and . Wiese, Flows and stochastic Taylor series in Itô calculus, Journal of Physics A: Mathematical and Theoretical, vol.48, issue.49, p.495202, 2015.

A. M. Etheridge and C. Labbé, Scaling limits of weakly asymmetric interfaces, Communications in Mathematical Physics, vol.336, issue.1, pp.287-336, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00957495

M. Errami, F. Russo, and P. Vallois, Itô's formula for C 1 ?-functions of a càdlàg process and related calculus. Probability Theory and Related Fields, vol.122, p.191, 2002.

H. E. Altman and L. Zambotti, Bessel SPDEs and renormalized local times, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01910713

P. K. Friz, B. Gess, A. Gulisashvili, and S. Riedel, The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory. The Annals of Probability, vol.44, pp.684-738, 2016.

P. Friz and M. Hairer, A Course on Rough Paths: With an Introduction to Regularity Structures, 2014.

F. Fauvet and F. Menous, Ecalle's arborification coarborification transforms and Connes-Kreimer Hopf algebra. Annales scientifiques de l'ENS, vol.50, pp.39-83, 2017.

H. Föllmer, Calcul d'Ito sans probabilités, vol.15, pp.143-150, 1981.

M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet forms and symmetric Markov processes, De Gruyter Studies in Mathematics, vol.19, 2011.

F. Flandoli and F. Russo, Generalized Integration and Stochastic ODEs, Annals of Probability, vol.30, issue.1, pp.270-292, 2002.

T. Funaki, Random motion of strings and related stochastic evolution equations, Nagoya Mathematical Journal, vol.89, pp.129-193, 1983.

P. Friz and N. Victoir, Differential equations driven by Gaussian signals, Ann. Inst. Henri Poincaré Probab. Stat, vol.46, issue.2, pp.369-413, 2010.

K. Peter, N. B. Friz, and . Victoir, Multidimensional stochastic processes as rough paths, Cambridge Studies in Advanced Mathematics, vol.120, 2010.

D. Geman and J. Horowitz, Occupation Densities, Annals of Probability, vol.8, issue.1, pp.1-67, 1980.

M. Gerencsér and M. Hairer, Singular SPDEs in domains with boundaries, 2017.

M. Gubinelli, P. Imkeller, and N. Perkowski, Paracontrolled distributions and singular PDEs, Forum of Mathematics, Pi, vol.3, 2015.

M. Gradinaru, I. Nourdin, F. Russo, and P. Vallois, m-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.41, issue.4, pp.781-806, 2005.

M. Gradinaru, I. Nourdin, and S. Tindel, Ito's-and Tanaka'stype formulae for the stochastic heat equation: The linear case, Journal of Functional Analysis, vol.228, pp.114-143, 2005.

M. Gradinaru, F. Russo, and P. Vallois, Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H ? 1 4 . The Annals of Probability, vol.31, pp.1772-1820, 2003.

M. Gubinelli, Controlling rough paths, Journal of Functional Analysis, vol.216, issue.1, pp.86-140, 2004.

M. Gubinelli, Ramification of rough paths, Journal of Differential Equations, vol.248, issue.4, pp.693-721, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00143655

G. Lajos-gergely, Differential equations driven by ?-rough paths, Proceedings of the Edinburgh Mathematical Society, vol.59, issue.3, pp.741-758, 2016.

M. Hairer, Rough stochastic PDEs, Communications on Pure and Applied Mathematics, vol.64, issue.11, pp.1547-1585, 2011.

M. Hairer, Solving the KPZ equation, Annals of Mathematics, vol.178, issue.2, pp.559-664, 2013.

M. Hairer, A theory of regularity structures. Inventiones mathematicae, vol.198, pp.269-504, 2014.

M. Hairer, Introduction to regularity structures, Brazilian Journal of Probability and Statistics, vol.29, issue.2, pp.175-210, 2015.

M. Hairer, The motion of a random string, 2016.

M. E. Hoffman and K. Ihara, Quasi-shuffle products revisited, Journal of Algebra, vol.481, pp.293-326, 2017.

M. Hairer and D. Kelly, Geometric versus non-geometric rough paths, Ann. Inst. H. Poincaré Probabilité et Statistique, vol.51, issue.1, p.2015

M. E. Hoffman, Quasi-Shuffle Products, Journal of Algebraic Combinatorics, vol.11, issue.1, pp.49-68, 2000.

M. Hairer and . Pardoux, A Wong-Zakai theorem for stochastic PDEs, Journal of the Mathematical Society of Japan, vol.67, issue.4, pp.1551-1604, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01231762

M. Hairer and H. Weber, Rough Burgers-like equations with multiplicative noise. Probability Theory and Related Fields, vol.155, pp.71-126, 2013.

K. Itô, Differential equations determining Markov processes, Zenkoku Shijo Sugaku Danwakai, vol.1077, pp.1352-1400, 1942.

K. Itô, Stochastic integral, Proceedings of the Imperial Academy of Tokyo, vol.20, pp.519-524, 1944.

D. Kelly, Itô corrections in stochastic equations, 2012.

M. Kardar, G. Parisi, and Y. Zhang, Dynamic Scaling of Growing Interfaces, Physical Review Letters, vol.56, pp.889-892, 1986.

N. V. Krylov, Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate studies in mathematics, American Mathematical Society, 1996.

A. Lanconelli, On a new version of the Itô's formula for the stochastic heat equation, Communications on Stochastic Analysis, vol.1, issue.2, pp.311-320, 2007.

M. Lothaire, Combinatorics on words. Cambridge Mathematical Library, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00620609

T. Lyons and N. Victoir, Annales de l'Institut Henri Poincaré, Analyse Non Linéaire, vol.24, issue.5, pp.835-847, 2007.

R. C. Lyndon, On burnside's problem, Transactions of the American Mathematical Society, vol.77, issue.2, pp.202-215, 1954.

T. J. Lyons, Differential equations driven by rough signals, Revista Matemática Iberoamericana, vol.14, issue.2, pp.215-310, 1998.

D. Manchon, Hopf algebras, from basics to applications to renormalization, 2004.

G. Melançon and C. Reutenauer, Lyndon words, free algebras and shuffles, Canadian Journal of Mathematics. Journal Canadien de Mathématiques, vol.41, issue.4, pp.577-591, 1989.

C. Mueller and R. Tribe, Hitting properties of a random string, Electronic Journal of Probability, vol.7, issue.10, 2002.

I. Nourdin and D. Nualart, Central Limit Theorems for Multiple Skorokhod integrals, Journal of Theoretical Probability, vol.23, issue.1, pp.39-64, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00469195

D. Nualart, The Malliavin Calculus and Related Topics. Probability and its applications, 1995.

D. Nualart and M. Zakai, Generalized multiple stochastic integrals and the representation of Wiener functionals, Stochastics, vol.23, issue.3, pp.311-330, 1998.

G. Peccati and M. Taqqu, Wiener Chaos: Moments, Cumulants and Diagrams, 2011.

C. Reutenauer, Free Lie Algebras. LMS monographs, 1993.

F. Russo and C. A. Tudor, On bifractional Brownian motion, Stochastic Processes and their Applications, vol.116, pp.830-856, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00130627

F. Russo and P. Vallois, Forward, Backward and Symmetric Stochastic integration. Probability Theory and Related Fields, vol.97, pp.403-421, 1993.

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

D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Grundlehren der mathematischen Wissenschaften, 2004.

L. Schwartz, Sur l'impossibilité de la multiplication des distributions. Comptes Rendus de l'Académie des sciences de Paris, vol.239, pp.847-848, 1954.

L. Simon, Schauder estimates by scaling, Calculus of Variations and Partial Differential Equations, vol.5, issue.5, pp.391-407, 1997.

R. Stratonovich, A new representation for stochastic integrals and equations, SIAM Journal on Control, vol.4, issue.2, pp.362-371, 1966.

J. Swanson, Variations of the solution to a stochastic heat equation, Annals of Probability, vol.35, issue.6, pp.2122-2159, 2007.

N. Tapia and L. Zambotti, The geometry of the space of branched Rough Paths. arXiv preprint 1810.12179v3, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01908559

J. B. Walsh, An introduction to stochastic partial differential equations.École d'été de probabilités de Saint-Flour, XIV -1984, 1984.

W. H. Young, An inequality of the Hölder type, connected with Stieltjes integration, Acta Mathematica, vol.67, issue.1, pp.251-282, 1936.

L. Zambotti, A reflected stochastic heat equation as symmetric dynamics with respect to the 3-d Bessel bridge, Journal of Functional Analysis, vol.180, issue.1, pp.195-209, 2001.

L. Zambotti, Itô-tanaka's formula for stochastic partial differential equations driven by additive space-time white noise, Stochastic partial differential equations and applications -VII, vol.245, pp.337-347, 2006.

L. Zambotti, Random Obstacle Problems.École d'été de probabilités de Saint-Flour, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01725285