Publications

1. Arnaudon, Marc; Nielsen, Frank
   On Approximating the Riemannian 1-Center.
   Computational Geometry: Theory and Applications, to appear
2. Arnaudon, Marc; Dombry, Clément; Phan, Anthony; Yang, Le
   Stochastic algorithms for computing means of probability measures.
   Stochastic Processes and their Applications122 (2012), pp. 1437-1455
3. Arnaudon, Marc; Nielsen, Frank
   Medians and means in Finsler geometry.
   LMS Journal of Computation and Mathematics volume 15, pp. 23-37 (2012)
4. Arnaudon, Marc; Cruzeiro, Ana Bela; Galamba, Nuno
   Lagrangian Navier-Stokes flows: a stochastic model.
   Journal of Physics A: Mathematical and Theoretical, 44 (2011), no. 17, 175501, 12 pp
5. Arnaudon, Marc; Thalmaier, Anton
   The differentiation of hypoelliptic diffusion semigroups.
   Illinois Journal of Math., to appear
6. Arnaudon, Marc; Cruzeiro, Ana Bela
   Stochastic Lagrangian flows on some compact manifolds.
   Stochastics An International Journal of Probability and Stochastic Processes, Vol. 84, Nos 2-3, April-June 2012, 367--381
7. Arnaudon, Marc; Thalmaier, Anton
   Brownian motion and negative curvature.
   Boundaries and Spectra of Random Walks, Progress in Probability, Vol. 64, 145--163, Springer Basel (2011)
8. Arnaudon, Marc; Thalmaier, Anton
   Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis.
   Advanced Studies in Pure Mathematics 57 (2010) 29--48
9. Arnaudon, Marc; Coulibaly, Abdoulaye, Thalmaier, Anton
   Horizontal diffusions in C^1 path space.
   Séminaire de Probabilités XLIII, 73--94, Lecture Notes in Mathematics 2006, Springer (2010)
10. Arnaudon, Marc; Thalmaier, Anton; Wang, Feng-Yu
    Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds.
    Stochastic Processes and their Applications, 119 (2009), no. 10, 3653--3670.
11. Arnaudon, Marc; Breton, Jean-Christophe ; Privault, Nicolas
    convex ordering for random vectors using predictable representation.
    Potential Analysis, 29 (2008), no. 4, 327--349.
12. Arnaudon, Marc; Thalmaier, Anton ; Ulsamer, Stefanie
    Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature.
    Mathematische Zeitschrifft, 263 (2009), no. 2, 369--409.
13. Arnaudon, Marc; Coulibaly, Koléhé Abdoulaye ; Thalmaier, Anton
    Brownian motion with respect to a metric depending on time: definition, existence and applications to Ricci flow.
    C. R. Acad. Sci. Paris, 346 (2008) no. 13--14, 773--778.
14. Arnaudon, Marc; Driver, Bruce K.; Thalmaier, Anton
    Gradient estimates for positive harmonic functions by stochastic analysis.
    Stochastic Processes and their Applications, 117 (2007), no. 2, 202--220.
15. Arnaudon, Marc; Thalmaier, Anton; Wang, Feng-Yu
    Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below.
    Bull. Sci. Math. 130 (2006) 223--233
16. Arnaudon, Marc; Simon, Thomas
    Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature.
    Annales de l'institut Fourier 55 (2005), no. 3, 891--930.
17. Arnaudon, Marc; Li, Xue-Mei
    Barycentres of measures transported by stochastic flows.
    Ann. Probab. 33 (2005), no. 4, 1509--1543.
18. Arnaudon, Marc; Plank, Holger; Thalmaier, Anton
    A Bismut type formula for the Hessian of heat semigroups.
    C. R. Math. Acad. Sci. Paris 336 (2003), no. 8, 661--666. 58J65 (60G44)
19. Arnaudon, Marc; Thalmaier, Anton
    Horizontal martingales in vector bundles.
    Séminaire de Probabilités, XXXVI, 419--456, Lecture Notes in Math., 1801, Springer, Berlin, 2003. 58J65 (60G48)
20. Arnaudon, Marc; Thalmaier, Anton
    Yang-Mills fields and random holonomy along Brownian bridges.
    Ann. Probab. 31 (2003), no. 2, 769--790. 58J65 (60H07 60H30 81T13)
21. Arnaudon, Marc; Bauer, Robert O.; Thalmaier, Anton
    A probabilistic approach to the Yang-Mills heat equation.
    J. Math. Pures Appl. (9) 81 (2002), no. 2, 143--166. 58J65 (58J35 60J65)
22. Arnaudon, Marc; Belopolskaya, Yana; Paycha, Sylvie
    Renormalized Laplacians on a class of Hilbert manifolds and a Bochner-Weitzenb�ck type formula for current groups.
    Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), no. 1, 53--98. 58J65 (35J05 35R15 46T20)
23. Arnaudon, Marc; Thalmaier, Anton
    Bismut type differentiation of semigroups.
    Prob. Theory and Math. Stat. (Vilnius, 1998), 23-32, VSP/TEV, Utrecht and Vilnius, 1999
24. Arnaudon, M.
    Appendix to the preceding paper: "A remark on Tsirelson's stochastic differential equation" [in Séminaire de Probabilités, XXXIII, 291--303, Lecture Notes in Math., 1709, Springer, Berlin, 1999; MR 2001e:60111] by M. �mery and W. Schachermayer. Natural filtration of Brownian motion indexed by R in a compact manifold.
    (French) Séminaire de Probabilités, XXXIII, 304--314, Lecture Notes in Math., 1709, Springer, Berlin, 1999. 60J65
25. Arnaudon, Marc; Li, Xue-Mei; Thalmaier, Anton
    Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps.
    Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), no. 6, 765--791. 58J65 (58E20 60G48)
26. Arnaudon, Marc; Thalmaier, Anton
    Stability of stochastic differential equations in manifolds.
    Séminaire de Probabilités, XXXII, 188--214, Lecture Notes in Math., 1686, Springer, Berlin, 1998. 60H10 (58G32)
27. Arnaudon, M.; Thalmaier, A.
    Complete lifts of connections and stochastic Jacobi fields.
    J. Math. Pures Appl. (9) 77 (1998), no. 3, 283--315. 58G32 (60H30)
28. Arnaudon, M.; Paycha, S.
    Regularisable and minimal orbits for group actions in infinite dimensions.
    Comm. Math. Phys. 191 (1998), no. 3, 641--662. 58D19 (22E65 58G26)
29. Arnaudon, M.; Paycha, S.
    Stochastic tools on Hilbert manifolds: interplay with geometry and physics.
    Comm. Math. Phys. 187 (1997), no. 2, 243--260. 58G32 (58B20 60H30)
30. Arnaudon, Marc
    Differentiable and analytic families of continuous martingales in manifolds with connection.
    Probab. Theory Related Fields 108 (1997), no. 2, 219--257. 58G32 (60G44)
31. Paycha, S.; Arnaudon, M.
    Projections de mouvements browniens régularisés via l'action d'un groupe de Lie hilbertien.
    (French) [Projections of regularized Brownian motions via the action of a Hilbert-Lie group] Ann. Math. Blaise Pascal 3 (1996), no. 1, 103--110. 60J60 (58B25 58G32)
32. Arnaudon, Marc
    Barycentres convexes et approximations des martingales continues dans les variétés.
    (French) [Convex barycenters and approximations of continuous martingales] Séminaire de Probabilités, XXIX, 70--85, Lecture Notes in Math., 1613, Springer, Berlin, 1995. 58G32 (60G44)
33. Arnaudon, M.; Paycha, S.
    Factorisation of semi-martingales on principal fibre bundles and the Faddeev-Popov procedure in gauge theories.
    Stochastics Stochastics Rep. 53 (1995), no. 1-2, 81--107. 58G32 (58D20 60H99)
34. Arnaudon, Marc
    Espérances conditionnelles et $\scr C$-martingales dans les variétés.
    (French) [Conditional expectations and $\scr C$-martingales in manifolds] Séminaire de Probabilités, XXVIII, 300--311, Lecture Notes in Math., 1583, Springer, Berlin, 1994. 58G32 (60G48)
35. Arnaudon, Marc
    Comportements de martingales et de semi-martingales dans des variétés.
    (French) [Behavior of martingales and semimartingales in manifolds] Thèse, Université Louis Pasteur, Strasbourg, 1994. Prépublication de l'Institut de Recherche Mathématique Avancée [Prepublication of the Institute of Advanced Mathematical Research], 1993/37. Université Louis Pasteur, Département de Mathématique, Institut de Recherche Mathématique Avancée, Strasbourg, 1993. 140 pp. 58G32 (60G48)
36. Arnaudon, Marc
    Propriétés asymptotiques des semi-martingales à valeurs dans des variétés à bord continu.
    (French) [Asymptotic properties of semimartingales with values in manifolds with continuous boundary] Séminaire de Probabilités, XXVII, 182--201, Lecture Notes in Math., 1557, Springer, Berlin, 1993. 58G32 (60G48)
37. Arnaudon, Marc
    Dédoublement des variétés à bord et des semi-martingales.
    (French) [Doubling of manifolds with boundary and semimartingales] Stochastics Stochastics Rep. 44 (1993), no. 1-2, 43--63. 58G32 (60G44)
38. Arnaudon, Marc
    Semi-martingales dans les espaces homogènes.
    (French) [Semimartingales in homogeneous spaces] Ann. Inst. H. Poincaré Probab. Statist. 29 (1993), no. 2, 269--288. 58G32 (60G44)
39. Arnaudon, Marc
    Caractéristiques locales des semi-martingales et changements de probabilités.
    (French) [Local characteristics of semimartingales and change of probabilities] Ann. Inst. H. Poincaré Probab. Statist. 29 (1993), no. 2, 251--267. 60G44 (58G32 60G30)
40. Arnaudon, Marc
    Propriétés asymptotiques des semi-martingales à valeurs dans des variétés à bord peu régulier.
    (French) [Asymptotic properties of semimartingales with values in manifolds with nonsmooth boundary] C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 7, 717--722. 60G44 (58G32)
41. Arnaudon, Marc
    Connexions et martingales dans les groupes de Lie.
    (French) [Connections and martingales in Lie groups] With an appendix by Pierre Mathieu and the author. Lecture Notes in Math., 1526, Séminaire de Probabilités, XXVI, 146--156, Springer, Berlin, 1992. 58G32 (22E99 60G44)
42. Arnaudon, Marc
    Caractéristiques locales des semi-martingales et changements de probabilités.
    (French) [Local characteristics of semimartingales and changes of probabilities] C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 4, 175--178. 60G44 (60B15 60H07 60J60)