. , 1.1 Martingales with prescribed terminal values on manifolds, p.28

. , 3.1 A stochastic algorithm obtained with parallel coupling, vol.55

. , 56 II.4.2 Main property satisfied by X h,? (a)

. .. Bsdes, 4.3 Stability result for the diagonal quadratic case

. .. Bibliography,

, If f is a deterministic function, then the assumption (Df,b) is not required

M. Arnaudon, X. Li, and A. Thalmaier, Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol.35, issue.6, pp.765-791, 1999.

M. Arnaudon, Barycentres convexes et approximations des martingales continues dans les variétés, Séminaire de Probabilités, XXIX, pp.70-85, 1995.

M. Arnaudon, Differentiable and analytic families of continuous martingales in manifolds with connection. Probability Theory and Related Fields, vol.108, pp.219-257, 1997.

M. Arnaudon and A. Thalmaier, Complete lifts of connections and stochastic Jacobi fields, Journal de Mathématiques Pures et Appliquées, vol.77, issue.3, pp.283-315, 1998.

M. Arnaudon and A. Thalmaier, Stability of stochastic differential equations in manifolds, Séminaire de Probabilités, XXXII, pp.188-214, 1998.

M. Arnaudon and A. Thalmaier, Horizontal martingales in vector bundles, Séminaire de Probabilités XXXVI, pp.419-456, 2003.

R. Bañuelos and A. Bennett, Paraproducts and commutators of martingale transforms, Proceedings of the American Mathematical Society, vol.103, issue.4, pp.1226-1234, 1988.

P. Briand and R. Elie, A simple constructive approach to quadratic BSDEs with or without delay, Stochastic Processes and their Applications, vol.123, pp.2921-2939, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00717226

P. Barrieu and N. E. Karoui, Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs. The Annals of Probability, vol.41, pp.1831-1863, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00560153

P. Briand and Y. Hu, BSDE with quadratic growth and unbounded terminal value. Probability Theory and Related Fields, vol.136, pp.604-618, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00004619

J. Bismut, Conjugate convex functions in optimal stochastic control, Journal of Mathematical Analysis and Applications, vol.44, issue.2, pp.384-404, 1973.

F. Blache, Backward stochastic differential equations on manifolds. Probability Theory and Related Fields, vol.132, pp.391-437, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00003918

F. Blache, Equations différentielles stochastiques rétrogrades à valeurs sur les variétés. www.theses.fr, 2004.

F. Blache, Backward stochastic differential equations on manifolds II. Probability Theory and Related Fields, vol.136, pp.234-262, 2006.

J. Bielagk, A. Lionnet, and G. Reis, Equilibrium pricing under relative performance concerns. arXiv.org, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01245812

B. Chikvinidze and M. Mania, New Proofs of Some Results on Bounded Mean Oscillation Martingales Using Backward Stochastic Differential Equations, Journal of Theoretical Probability, vol.27, issue.4, pp.1213-1228, 2013.

P. Cheridito and K. Nam, Multidimensional quadratic and subquadratic BSDEs with special structure, vol.87, pp.871-884, 2015.

W. Richard and . Darling, Martingales in manifolds-definition, examples, and behaviour under maps, Seminar on Probability, XVI, Supplement, pp.217-236, 1982.

W. Richard and . Darling, Constructing gamma-martingales with prescribed limit, using backwards SDE. The Annals of Probability, vol.23, pp.1234-1261, 1995.

F. Delbaen, Y. Hu, and A. Richou, On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol.47, issue.2, pp.559-574, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00391112

F. Delbaen and S. Tang, Harmonic analysis of stochastic equations and backward stochastic differential equations. Probability Theory and Related Fields, vol.146, pp.291-336, 2008.

T. Duncan, Stochastic integrals in Riemann manifolds, Journal of Multivariate Analysis, vol.6, issue.3, pp.397-413, 1976.

N. E. Karoui and S. Hamadène, BSDEs and risk-sensitive control, zerosum and nonzero-sum game problems of stochastic functional differential equations, Stochastic Processes and their Applications, vol.107, pp.145-169, 2003.

N. E. Karoui, S. Peng, and M. Quenez, Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997.

M. Emery and . Mokobodzki, Sur le barycentre d'une probabilité dans une variété, Séminaire de Probabilités, XXV, pp.220-233, 1991.

M. Emery, Stabilité des solutions des équations différentielles stochastiques application aux intégrales multiplicatives stochastiques. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.41, pp.241-262, 1978.

M. Emery, Stochastic calculus in manifolds, 1989.

M. Emery, Martingales continues dans les variétés différentiables, 1999.

R. Elie and D. Possamaï, Contracting theory with competitive interacting agents. arXiv.org, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01481381

G. E. Espinosa and N. Touzi, Optimal investment under relative performance concerns, Mathematical Finance, vol.25, issue.2, pp.221-257, 2015.

C. Frei and G. Reis, A financial market with interacting investors: does an equilibrium exist?, Mathematics and Financial Economics, vol.4, issue.3, pp.161-182, 2011.

C. Frei, Splitting multidimensional BSDEs and finding local equilibria, Stochastic Processes and their Applications, vol.124, pp.2654-2671, 2014.

S. Geiss and J. Ylinen, Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs. arXiv.org, 2014.

Y. Hu and S. Tang, Multi-dimensional backward stochastic differential equations of diagonally quadratic generators, Stochastic Processes and their Applications, vol.126, pp.1066-1086, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01058817

A. Jamneshan, M. Kupper, and P. Luo, Multidimensional quadratic BSDEs with separated generators. arXiv.org, 2014.

N. Kazamaki, Continuous exponential martingales and BMO, Lecture Notes in Mathematics, vol.1579, 1994.

S. Wilfrid and . Kendall, Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence, Proceedings of the London Mathematical Society, issue.2, pp.371-406, 1990.

S. Wilfrid and . Kendall, Convexity and the hemisphere, Journal of the London Mathematical Society. Second Series, vol.43, issue.3, pp.567-576, 1991.

S. Wilfrid and . Kendall, Convex geometry and nonconfluent ?-martingales. II. Wellposedness and ?-martingale convergence, Stochastics and Stochastic Reports, vol.38, issue.3, pp.135-147, 1992.

S. Wilfrid and . Kendall, The Propeller: A Counterexample to a Conjectured Criterion for the Existence of Certain Convex Functions, Journal of the London Mathematical Society. Second Series, issue.2, pp.364-374, 1992.

M. Kobylanski, Backward stochastic differential equations and partial differential equations with quadratic growth, Annals of Probability, 2000.

D. Kramkov and S. Pulido, A system of quadratic BSDEs arising in a price impact model, The Annals of Applied Probability, vol.26, issue.2, pp.794-817, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01147411

D. Kramkov and S. Pulido, Stability and Analytic Expansions of Local Solutions of Systems of Quadratic BSDEs with Applications to a Price Impact Model, SIAM J. Financial Math, vol.7, issue.1, pp.567-587, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01181147

C. Kardaras, H. Xing, and G. ?itkovi´c?itkovi´c, Incomplete stochastic equilibria with exponential utilities close to Pareto optimality, 2015.

A. L. Brigant, Computing distances and geodesics between manifold-valued curves in the SRV framework, Journal of Geometric Mechanics, vol.9, issue.2, pp.131-156, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01253495

C. Lobry, Et pourtant... ils ne remplissent pas N, 1989.

P. Luo and L. Tangpi, Solvability of coupled FBSDEs with quadratic and superquadratic growth. arXiv.org, 2015.

P. Meyer, A differential geometric formalism for the ito calculus, Stochastic Integrals, pp.256-270, 1981.

P. Meyer, Geometrie stochastique sans larmes, Séminaire de Probabilités XV 1979/80, pp.44-102, 1981.

P. Meyer, Géometrie différentielle stochastique. II. In Lecture Notes in Math, pp.165-207, 1982.

C. Marinelli and M. Röckner, On the maximal inequalities of Burkholder, Davis and Gundy, Expositiones Mathematicae, vol.34, issue.1, pp.1-26, 2016.

D. Nualart, The Malliavin calculus and related topics. Probability and its Applications, 2006.

J. Picard, Martingales on Riemannian manifolds with prescribed limit, Journal of Functional Analysis, vol.99, issue.2, pp.223-261, 1991.

J. Picard, Barycentres et martingales sur une variété, Probabilités et Statistiques, vol.30, issue.4, pp.647-702, 1994.

J. Picard, Martingales sur le cercle, Séminaire de Probabilités XXXII, pp.147-160, 2006.

E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems and Control Letters, vol.14, issue.1, pp.55-61, 1990.

W. Schachermayer, A characterisation of the closure of Hin f ty in BMO. Séminaire de Probabilités de Strasbourg, 1996.

R. Tevzadze, Solvability of backward stochastic differential equations with quadratic growth, Stochastic Processes and their Applications, vol.118, pp.503-515, 2008.

H. Xing and G. ?itkovi´c?itkovi´c, A class of globally solvable Markovian quadratic BSDE systems and applications. arXiv.org, 2016.

S. Kentar¯-o-yano and . Ishihara, Tangent and cotangent bundles. differential geometry, 1973.