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) ,
4.3 Stability result for the diagonal quadratic case ,
,
, If f is a deterministic function, then the assumption (Df,b) is not required
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. ,
Barycentres convexes et approximations des martingales continues dans les variétés, Séminaire de Probabilités, XXIX, pp.70-85, 1995. ,
Differentiable and analytic families of continuous martingales in manifolds with connection. Probability Theory and Related Fields, vol.108, pp.219-257, 1997. ,
Complete lifts of connections and stochastic Jacobi fields, Journal de Mathématiques Pures et Appliquées, vol.77, issue.3, pp.283-315, 1998. ,
Stability of stochastic differential equations in manifolds, Séminaire de Probabilités, XXXII, pp.188-214, 1998. ,
Horizontal martingales in vector bundles, Séminaire de Probabilités XXXVI, pp.419-456, 2003. ,
Paraproducts and commutators of martingale transforms, Proceedings of the American Mathematical Society, vol.103, issue.4, pp.1226-1234, 1988. ,
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
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
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
Conjugate convex functions in optimal stochastic control, Journal of Mathematical Analysis and Applications, vol.44, issue.2, pp.384-404, 1973. ,
, 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
Equations différentielles stochastiques rétrogrades à valeurs sur les variétés. www.theses.fr, 2004. ,
, Backward stochastic differential equations on manifolds II. Probability Theory and Related Fields, vol.136, pp.234-262, 2006.
, Equilibrium pricing under relative performance concerns. arXiv.org, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01245812
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. ,
Multidimensional quadratic and subquadratic BSDEs with special structure, vol.87, pp.871-884, 2015. ,
Martingales in manifolds-definition, examples, and behaviour under maps, Seminar on Probability, XVI, Supplement, pp.217-236, 1982. ,
Constructing gamma-martingales with prescribed limit, using backwards SDE. The Annals of Probability, vol.23, pp.1234-1261, 1995. ,
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
Harmonic analysis of stochastic equations and backward stochastic differential equations. Probability Theory and Related Fields, vol.146, pp.291-336, 2008. ,
Stochastic integrals in Riemann manifolds, Journal of Multivariate Analysis, vol.6, issue.3, pp.397-413, 1976. ,
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. ,
Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997. ,
Sur le barycentre d'une probabilité dans une variété, Séminaire de Probabilités, XXV, pp.220-233, 1991. ,
, Stabilité des solutions des équations différentielles stochastiques application aux intégrales multiplicatives stochastiques. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.41, pp.241-262, 1978.
Stochastic calculus in manifolds, 1989. ,
Martingales continues dans les variétés différentiables, 1999. ,
, Contracting theory with competitive interacting agents. arXiv.org, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01481381
Optimal investment under relative performance concerns, Mathematical Finance, vol.25, issue.2, pp.221-257, 2015. ,
A financial market with interacting investors: does an equilibrium exist?, Mathematics and Financial Economics, vol.4, issue.3, pp.161-182, 2011. ,
Splitting multidimensional BSDEs and finding local equilibria, Stochastic Processes and their Applications, vol.124, pp.2654-2671, 2014. ,
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs. arXiv.org, 2014. ,
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
Multidimensional quadratic BSDEs with separated generators. arXiv.org, 2014. ,
Continuous exponential martingales and BMO, Lecture Notes in Mathematics, vol.1579, 1994. ,
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. ,
Convexity and the hemisphere, Journal of the London Mathematical Society. Second Series, vol.43, issue.3, pp.567-576, 1991. ,
Convex geometry and nonconfluent ?-martingales. II. Wellposedness and ?-martingale convergence, Stochastics and Stochastic Reports, vol.38, issue.3, pp.135-147, 1992. ,
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. ,
Backward stochastic differential equations and partial differential equations with quadratic growth, Annals of Probability, 2000. ,
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
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
Incomplete stochastic equilibria with exponential utilities close to Pareto optimality, 2015. ,
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
Et pourtant... ils ne remplissent pas N, 1989. ,
, Solvability of coupled FBSDEs with quadratic and superquadratic growth. arXiv.org, 2015.
A differential geometric formalism for the ito calculus, Stochastic Integrals, pp.256-270, 1981. ,
Geometrie stochastique sans larmes, Séminaire de Probabilités XV 1979/80, pp.44-102, 1981. ,
, Géometrie différentielle stochastique. II. In Lecture Notes in Math, pp.165-207, 1982.
On the maximal inequalities of Burkholder, Davis and Gundy, Expositiones Mathematicae, vol.34, issue.1, pp.1-26, 2016. ,
, The Malliavin calculus and related topics. Probability and its Applications, 2006.
Martingales on Riemannian manifolds with prescribed limit, Journal of Functional Analysis, vol.99, issue.2, pp.223-261, 1991. ,
Barycentres et martingales sur une variété, Probabilités et Statistiques, vol.30, issue.4, pp.647-702, 1994. ,
Martingales sur le cercle, Séminaire de Probabilités XXXII, pp.147-160, 2006. ,
Adapted solution of a backward stochastic differential equation, Systems and Control Letters, vol.14, issue.1, pp.55-61, 1990. ,
A characterisation of the closure of Hin f ty in BMO. Séminaire de Probabilités de Strasbourg, 1996. ,
Solvability of backward stochastic differential equations with quadratic growth, Stochastic Processes and their Applications, vol.118, pp.503-515, 2008. ,
, A class of globally solvable Markovian quadratic BSDE systems and applications. arXiv.org, 2016.
Tangent and cotangent bundles. differential geometry, 1973. ,