Stochastic calculus and martingales on trees
Picard, Jean
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 631-683 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2005__41_4_631_0,
     author = {Picard, Jean},
     title = {Stochastic calculus and martingales on trees},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {631-683},
     doi = {10.1016/j.anihpb.2004.03.002},
     mrnumber = {2144228},
     zbl = {1077.60030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_4_631_0}
}

Picard, Jean. Stochastic calculus and martingales on trees. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 631-683. doi : 10.1016/j.anihpb.2004.03.002. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_4_631_0/

[1] R. Abraham, L. Serlet, Poisson snake and fragmentation, Electron. J. Probab. 7 (2002) 1-15, electronic. | MR 1943890 | Zbl 1015.60046

[2] M. Arnaudon, Barycentres convexes et approximations des martingales continues dans les variétés, in: Séminaire de Probabilités, XXIX, Lecture Notes in Math., vol. 1613, Springer, Berlin, 1995, pp. 70-85. | Numdam | MR 1459450 | Zbl 0837.58037

[3] M. Arnaudon, Differentiable and analytic families of continuous martingales in manifolds with connection, Probab. Theory Related Fields 108 (1997) 219-257. | MR 1452557 | Zbl 0883.60043

[4] M. Barlow, J. Pitman, M. Yor, On Walsh's Brownian motions, in: Séminaire de Probabilités, XXIII, Lecture Notes in Math., vol. 1372, Springer, Berlin, 1989, pp. 275-293. | Numdam | MR 1022917 | Zbl 0747.60072

[5] N. Bouleau, F. Hirsch, Dirichlet Forms and Analysis on Wiener Space, Studies in Mathematics, vol. 14, de Gruyter, 1991. | MR 1133391 | Zbl 0748.60046

[6] Z.Q. Chen, On reflected Dirichlet spaces, Probab. Theory Related Fields 94 (2) (1992) 135-162. | MR 1191106 | Zbl 0767.60073

[7] R.W.R. Darling, Martingales in manifolds - Definition, examples and behaviour under maps, in: Azéma J., Yor M. (Eds.), Séminaire de Probabilités, XVI, Supplément: Géométrie différentielle stochastique, Lecture Notes in Math., vol. 921, Springer, Berlin, 1982, pp. 217-236. | Numdam | MR 658727 | Zbl 0482.58035

[8] C. Dellacherie, P.A. Meyer, Probabilités et potentiel, Chapitres V à VIII, Hermann, 1980. | MR 566768 | Zbl 0464.60001

[9] J. Eells, B. Fuglede, Harmonic Maps between Riemannian Polyhedra, Cambridge Tracts in Mathematics, vol. 142, Cambridge University Press, Cambridge, 2001. | MR 1848068 | Zbl 0979.31001

[10] M. Émery, Stochastic Calculus in Manifolds, Universitext, Springer, 1989. | MR 1030543 | Zbl 0697.60060

[11] M. Émery, G. Mokobodzki, Sur le barycentre d'une probabilité dans une variété, in: Séminaire de Probabilités, XXV, Lecture Notes in Math., vol. 1485, Springer, Berlin, 1991, pp. 220-233. | Numdam | MR 1187782 | Zbl 0753.60046

[12] M. Émery, W.A. Zheng, Fonctions convexes et semimartingales dans une variété, in: Seminar on Probability, XVIII, Lecture Notes in Math., vol. 1059, Springer, Berlin, 1984, pp. 501-518. | Numdam | MR 770977 | Zbl 0543.58029

[13] S.N. Evans, Snakes and spiders: Brownian motion on R-trees, Probab. Theory Related Fields 117 (3) (2000) 361-386. | MR 1774068 | Zbl 0959.60070

[14] M. Fukushima, Y. Ōshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, vol. 19, Walter de Gruyter, Berlin, 1994. | MR 1303354 | Zbl 0838.31001

[15] J. Jost, Equilibrium maps between metric spaces, Calc. Var. Partial Differential Equations 2 (2) (1994) 173-204. | MR 1385525 | Zbl 0798.58021

[16] J. Jost, Riemannian Geometry and Geometric Analysis, Universitext, Springer-Verlag, Berlin, 1995. | MR 1351009 | Zbl 0828.53002

[17] J. Jost, Generalized Dirichlet forms and harmonic maps, Calc. Var. Partial Differential Equations 5 (1) (1997) 1-19. | MR 1424346 | Zbl 0868.31009

[18] W.S. Kendall, Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence, Proc. London Math. Soc. 61 (3) (1990) 371-406. | MR 1063050 | Zbl 0675.58042

[19] W.S. Kendall, Probability, convexity and harmonic maps II: Smoothness via probabilistic gradient inequalities, J. Funct. Anal. 126 (1) (1994) 226-257. | MR 1305069 | Zbl 0808.60058

[20] N.J. Korevaar, R.M. Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (3-4) (1993) 561-659. | MR 1266480 | Zbl 0862.58004

[21] W.B. Krebs, Brownian motion on the continuum tree, Probab. Theory Related Fields 101 (3) (1995) 421-433. | MR 1324094 | Zbl 0822.60069

[22] J.-F. Le Gall, A class of path-valued Markov processes and its applications to superprocesses, Probab. Theory Related Fields 95 (1) (1993) 25-46. | MR 1207305 | Zbl 0794.60076

[23] J.-F. Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Lectures in Mathematics, ETH Zürich, Birkhäuser Verlag, Basel, 1999. | MR 1714707 | Zbl 0938.60003

[24] P.A. Meyer, Géométrie stochastique sans larmes, in: Azéma J., Yor M. (Eds.), Séminaire de Probabilités, XV, Lecture Notes in Math., vol. 850, Springer, Berlin, 1981, pp. 44-102. | Numdam | MR 622555 | Zbl 0459.60046

[25] J. Picard, Martingales on Riemannian manifolds with prescribed limit, J. Funct. Anal. 99 (2) (1991) 223-261. | MR 1121614 | Zbl 0758.60051

[26] J. Picard, Barycentres et martingales sur une variété, Ann. Inst. Henri Poincaré Probab. Stat. 30 (4) (1994) 647-702. | Numdam | MR 1302764 | Zbl 0817.58047

[27] J. Picard, Smoothness of harmonic maps for hypoelliptic diffusions, Ann. Probab. 28 (2) (2000) 643-666. | MR 1782269 | Zbl 1044.58045

[28] J. Picard, The manifold valued Dirichlet problem for symmetric diffusions, Potential Anal. 14 (2001) 53-72. | MR 1810798 | Zbl 0970.58022

[29] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Grundlehren der Mathematischen Wissenschaften, vol. 293, Springer-Verlag, Berlin, 1991. | MR 1083357 | Zbl 0731.60002

[30] C. Stricker, Semimartingales et valeur absolue, in: Séminaire de Probabilités, XIII, Lecture Notes in Math., vol. 721, Springer, Berlin, 1979, pp. 472-477. | Numdam | MR 544816 | Zbl 0408.60048

[31] K.-T. Sturm, A semigroup approach to harmonic maps, preprint. | MR 2140797

[32] K.-T. Sturm, Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature, Ann. Probab. 30 (3) (2002) 1195-1222. | MR 1920105 | Zbl 1017.60050

[33] B. Tsirelson, Triple points: from non-Brownian filtrations to harmonic measures, Geom. Funct. Anal. 7 (6) (1997) 1096-1142. | MR 1487755 | Zbl 0902.31004

[34] J. Walsh, A diffusion with a discontinuous local time, Astérisque 52-53 (1978) 37-45.

[35] M. Yor, Some Aspects of Brownian Motion. Part II, Lectures in Mathematics, ETH Zürich, Birkhäuser Verlag, Basel, 1997. | MR 1442263 | Zbl 0880.60082