Clark–Ocone formulas and Poincaré inequalities on the discrete cube

Cécile Ané

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 1, page 101-137
  • ISSN: 0246-0203

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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 37.1 (2001): 101-137. <http://eudml.org/doc/77681>.

@article{Ané2001,
author = {Ané, Cécile},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Poincaré inequality; Clark-Ocone formula; continuous time random walk},
language = {eng},
number = {1},
pages = {101-137},
publisher = {Elsevier},
title = {Clark–Ocone formulas and Poincaré inequalities on the discrete cube},
url = {http://eudml.org/doc/77681},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Ané, Cécile
TI - Clark–Ocone formulas and Poincaré inequalities on the discrete cube
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2001
PB - Elsevier
VL - 37
IS - 1
SP - 101
EP - 137
LA - eng
KW - Poincaré inequality; Clark-Ocone formula; continuous time random walk
UR - http://eudml.org/doc/77681
ER -

References

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  2. 2 K Bichteler, J.-B Gravereaux, J Jacod, Malliavin Calculus for Processes with Jumps, Gordon and Breach, New York, 1987. Zbl0706.60057MR1008471
  3. 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. Zbl0890.60045MR1484557
  4. 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. Zbl0685.60056MR1052702
  5. 5 C Dellacherie, P.-A Meyer, Probabilités et potentiel, Hermann, Paris, 1980, Chapitres V à VIII. Théorie des martingales. [Martingale theory]. Zbl0464.60001MR566768
  6. 6 E.P Hsu, Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds, Comm. Math. Phys.Vol. 189 (1) (1997) 9-16. Zbl0892.58083MR1478528
  7. 7 J Jacod, A.N Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987. Zbl0635.60021MR959133
  8. 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. Zbl0701.60048MR1071538
  9. 9 J Picard, Formules de dualité sur l'espace de Poisson, Ann. Inst. H. Poincaré Probab. Statist.Vol. 32 (4) (1996) 509-548. Zbl0859.60045MR1411270
  10. 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. Zbl0851.60052MR1380764
  11. 11 Wu L., A new modified logarithmic Sobolev inequality for Poisson point processes and several applications, Probab. Theor. Relat. Fields (2000) to appear. Zbl0970.60093MR1800540

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