On logarithmic Sobolev inequalities for normal martingales

Nicolas Privault

Annales de la Faculté des sciences de Toulouse : Mathématiques (2000)

  • Volume: 9, Issue: 3, page 509-518
  • ISSN: 0240-2963

How to cite

top

Privault, Nicolas. "On logarithmic Sobolev inequalities for normal martingales." Annales de la Faculté des sciences de Toulouse : Mathématiques 9.3 (2000): 509-518. <http://eudml.org/doc/73524>.

@article{Privault2000,
author = {Privault, Nicolas},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {chaos representation property; entropy; -class; gradient operator; Azéma martingale; Clark formula},
language = {eng},
number = {3},
pages = {509-518},
publisher = {UNIVERSITE PAUL SABATIER},
title = {On logarithmic Sobolev inequalities for normal martingales},
url = {http://eudml.org/doc/73524},
volume = {9},
year = {2000},
}

TY - JOUR
AU - Privault, Nicolas
TI - On logarithmic Sobolev inequalities for normal martingales
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2000
PB - UNIVERSITE PAUL SABATIER
VL - 9
IS - 3
SP - 509
EP - 518
LA - eng
KW - chaos representation property; entropy; -class; gradient operator; Azéma martingale; Clark formula
UR - http://eudml.org/doc/73524
ER -

References

top
  1. [1] Ané ( C.). — Grandes déviations et inégalités fonctionnelles pour des processus de Markov à temps continu sur un graphe. Thèse, Université Paul Sabatier - Toulouse III, 2000. 
  2. [2] Ané ( C.) and Ledoux ( M.). — On logarithmic Sobolev inequalities for continuous time random walks on graphs. Probab. Theory Related Fields, 116(4):573-602, 2000. Zbl0964.60063MR1757600
  3. [3] Bobkov ( S.G.) and Ledoux ( M.). — On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures. J. Funct. Anal., 156(2):347-365, 1998. Zbl0920.60002MR1636948
  4. [4] Capitaine ( M.), Hsu ( E.P.) and Ledoux ( M.). — Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces. Electron. Comm. Probab., 2:71-81 (electronic), 1997. Zbl0890.60045MR1484557
  5. [5] Dellacherie ( C.), Maisonneuve ( B.) and Meyer ( P.A.). - Probabilités et Potentiel, volume 5. Hermann, 1992. MR488194
  6. [6] Émery ( M.). — On the Azéma martingales. In Séminaire de Probabilités XXIII, volume 1372 of Lecture Notes in Mathematics, pages 66-87. Springer Verlag, 1990. Zbl0753.60045MR1022899
  7. [7] Gross ( L.). — Logarithmic Sobolev inequalities. Amer. J. Math., 97(4):1061-1083, 1975. Zbl0318.46049MR420249
  8. [8] Ledoux ( M.). — Concentration of measure and logarithmic Sobolev inequalities. In Séminaire de Probabilités XXXIII, volume 1709 of Lecture Notes in Math., pages 120-216. Springer, 1999. Zbl0957.60016MR1767995
  9. [9] Ma ( J.), Protter ( Ph.) and San Martin ( J.). — Anticipating integrals for a class of martingales. Bernoulli, 4:81-114, 1998. Zbl0897.60058MR1611879
  10. [10] Meyer ( P.A.). — Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics. Springer-Verlag, 1993. Zbl0773.60098MR1222649
  11. [11] Privault ( N.). — Independence of a class of multiple stochastic integrals. In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996), pages 249-259. Birkhäuser, Basel, 1999. Zbl0937.60049MR1712245
  12. [12] Privault ( N.), Solé ( J.L.) and Vives ( J.). — Chaotic Kabanov formula for the Azéma martingales. Bernoulli, 6(4):633-651, 2000. Zbl1023.60046MR1777688
  13. [13] Wu ( L.). — L1 and modified logarithmic Sobolev inequalities and deviation inequalities for Poisson point processes. Preprint, 1998. MR1636948
  14. [14] Wu ( L.). — A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Relat. Fields, to appear, 2000. Zbl0970.60093MR1800540
  15. [15] Yor ( M.). - Some Aspects of Brownian Motion (Part II). Birkäuser, 1992. Zbl0880.60082MR1193919

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.