Clark-Ocone formulas and Poincaré inequalities on the discrete cube
Ané, Cécile
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001), p. 101-137 / Harvested from Numdam
Publié le : 2001-01-01
@article{AIHPB_2001__37_1_101_0,
     author = {An\'e, C\'ecile},
     title = {Clark-Ocone formulas and Poincar\'e inequalities on the discrete cube},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {37},
     year = {2001},
     pages = {101-137},
     zbl = {0978.60084},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2001__37_1_101_0}
}
Ané, Cécile. Clark-Ocone formulas and Poincaré inequalities on the discrete cube. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) pp. 101-137. http://gdmltest.u-ga.fr/item/AIHPB_2001__37_1_101_0/

1 C Ané, M Ledoux, On logarithmic sobolev inequalities for continuous time random walks on graphs, Probab. Theor. Relat. Fields Vol. 116 (4) (2000) 573-602. | MR 1757600 | Zbl 0964.60063

2 K Bichteler, J.-B Gravereaux, J Jacod, Malliavin Calculus for Processes with Jumps, Gordon and Breach, New York, 1987. | MR 1008471 | Zbl 0706.60057

3 M Capitaine, E.P Hsu, M Ledoux, Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces, Electron. Comm. Probab. Vol. 2 (1997) 71-81. | MR 1484557 | Zbl 0890.60045

4 E.A Carlen, É Pardoux, Differential calculus and integration by parts on Poisson space, in: Stochastics, Algebra and Analysis in Classical and Quantum Dynamics (Marseille, 1988), Kluwer, Dordrecht, 1990, pp. 63-73. | MR 1052702 | Zbl 0685.60056

5 C Dellacherie, P.-A Meyer, Probabilités et potentiel, Hermann, Paris, 1980, Chapitres V à VIII. Théorie des martingales. [Martingale theory]. | MR 566768

6 E.P Hsu, Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds, Comm. Math. Phys. Vol. 189 (1) (1997) 9-16. | MR 1478528 | Zbl 0892.58083

7 J Jacod, A.N Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987. | MR 959133 | Zbl 0635.60021

8 D Nualart, J Vives, Anticipative calculus for the Poisson process based on the Fock space, in: In Séminaire de Probabilités, XXIV, 1988/89, Springer, Berlin, 1990, pp. 154-165. | Numdam | MR 1071538 | Zbl 0701.60048

9 J Picard, Formules de dualité sur l'espace de Poisson, Ann. Inst. H. Poincaré Probab. Statist. Vol. 32 (4) (1996) 509-548. | Numdam | MR 1411270 | Zbl 0859.60045

10 N Privault, Chaotic and variational calculus in discrete and continuous time for the Poisson process, Stochastics Stochastics Rep. Vol. 51 (1-2) (1994) 83-109. | MR 1380764 | Zbl 0851.60052

11 Wu L., A new modified logarithmic Sobolev inequality for Poisson point processes and several applications, Probab. Theor. Relat. Fields (2000) to appear. | MR 1800540 | Zbl 0970.60093