Clark-Ocone formulas and Poincaré inequalities on the discrete cube
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 1, pp. 101-137. 
@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},
     pages = {101--137},
     publisher = {Elsevier},
     volume = {37},
     number = {1},
     year = {2001},
     zbl = {0978.60084},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2001__37_1_101_0/}
}
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Ané, Cécile. Clark-Ocone formulas and Poincaré inequalities on the discrete cube. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 1, pp. 101-137. http://www.numdam.org/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 | Zbl

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

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 | Zbl

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 | Zbl

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

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

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

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 | Zbl

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 | Zbl

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 | Zbl

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