Free Access
Issue
ESAIM: PS
Volume 10, September 2006
Page(s) 317 - 339
DOI https://doi.org/10.1051/ps:2006013
Published online 08 September 2006
  1. C. Ané and M. Ledoux, On logarithmic Sobolev inequalities for continuous time random walks on graphs. Probab. Theory Related Fields 116 (2000) 573–602. [CrossRef] [MathSciNet]
  2. C. Ané, Clark-Ocone formulas and Poincaré inequalities on the discrete cube. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 101–137. [CrossRef] [MathSciNet]
  3. D. Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes. Lectures on probability theory (Saint-Flour, 1992), Lect. Notes Math. 1581 (1994) 1–114.
  4. S. Boucheron, O. Bousquet, G. Lugosi and P. Massart, Moment inequalities for functions of independent random variables. Ann. Probab. 33 (2005) 514–560. [CrossRef] [MathSciNet]
  5. A.-S. Boudou, P. Caputo, P. Dai Pra and G. Posta, Spectral gap estimates for interacting particle systems via a Bochner type inequality. J. Funct. Anal. 232 (2006) 222–258. [CrossRef] [MathSciNet]
  6. S.G. Bobkov and M. Ledoux, On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures. J. Funct. Anal. 156 (1998) 347–365. [CrossRef] [MathSciNet]
  7. A.A. Borovkov, Limit laws for queueing processes in multichannel systems. Sibirsk. Mat. Ž. 8 (1967) 983–1004. [MathSciNet]
  8. S. Bobkov and P. Tetali, Modified Log-Sobolev Inequalities in Discrete Settings, Preliminary version appeared in Proc. of the ACM STOC 2003, pp. 287–296. Cf. http://www.math.gatech.edu/~tetali/, 2003.
  9. P. Brémaud, Markov chains, Gibbs fields, Monte Carlo simulation, and queues. Texts Appl. Math. 31 (1999) xviii+444.
  10. D. Chafaï and D. Concordet, A continuous stochastic maturation model, preprint arXiv math.PR/0412193 or CNRS HAL ccsd-00003498, 2004.
  11. D. Chafaï, Entropies, convexity, and functional inequalities: on Formula -entropies and Formula -Sobolev inequalities. J. Math. Kyoto Univ. 44 (2004) 325–363. [MathSciNet]
  12. M.F. Chen, Variational formulas of Poincaré-type inequalities for birth-death processes. Acta Math. Sin. (Engl. Ser.) 19 (2003) 625–644.
  13. P. Caputo and G. Posta, Entropy dissipation estimates in a Zero-Range dynamics, preprint arXiv math.PR/0405455, 2004.
  14. P. Dai Pra and G. Posta, Logarithmic Sobolev inequality for zero-range dynamics: independence of the number of particles. Ann. Probab. 33 (2005) 2355–2401. [CrossRef] [MathSciNet]
  15. P. Dai Pra and G. Posta, Logarithmic Sobolev inequality for zero-range dynamics. Electron. J. Probab. 10 (2005) 525–576. [MathSciNet]
  16. P. Dai Pra, A.M. Paganoni and G. Posta, Entropy inequalities for unbounded spin systems. Ann. Probab. 30 (2002), 1959–1976.
  17. P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 (1996) 695–750. [CrossRef] [MathSciNet]
  18. S.N. Ethier and T.G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 1986, Characterization and convergence.
  19. S. Goel, Modified logarithmic Sobolev inequalities for some models of random walk. Stochastic Process. Appl. 114 (2004) 51–79. [CrossRef] [MathSciNet]
  20. O. Johnson and C. Goldschmidt, Preservation of log-concavity on summation, preprint arXiv math.PR/0502548, 2005.
  21. A. Joulin, On local Poisson-type deviation inequalities for curved continuous time Markov chains, with applications to birth-death processes, personal communication, preprint 2006.
  22. A. Joulin and N. Privault, Functional inequalities for discrete gradients and application to the geometric distribution. ESAIM Probab. Stat. 8 (2004) 87–101 (electronic). [CrossRef] [EDP Sciences]
  23. S. Karlin and J. McGregor, Linear growth birth and death processes. J. Math. Mech. 7 (1958) 643–662.
  24. F.P. Kelly, Blocking probabilities in large circuit-switched networks. Adv. in Appl. Probab. 18 (1986) 473–505. [CrossRef]
  25. F.P. Kelly, Loss networks. Ann. Appl. Probab. 1 (1991) 319–378. [CrossRef]
  26. C. Kipnis and C. Landim, Scaling limits of interacting particle systems. Fundamental Principles of Mathematical Sciences 320, Springer-Verlag, Berlin (1999).
  27. R. Latała and K. Oleszkiewicz, Between Sobolev and Poincaré, Geometric aspects of functional analysis. Lect. Notes Math. 1745 (2000) 147–168. [CrossRef]
  28. P. Massart, Concentration inequalities and model selection, Lectures on probability theory and statistics (Saint-Flour, 2003), available on the author's web-site http://www.math.u-psud.fr/~massart/stf2003_massart.pdf.
  29. Y. Mao, Logarithmic Sobolev inequalities for birth-death process and diffusion process on the line. Chinese J. Appl. Probab. Statist. 18 (2002) 94–100. [MathSciNet]
  30. L. Miclo, An example of application of discrete Hardy's inequalities. Markov Process. Related Fields 5 (1999) 319–330. [MathSciNet]
  31. Ph. Robert, Stochastic networks and queues, french ed., Applications of Mathematics (New York) 52, Springer-Verlag, Berlin, 2003, Stochastic Modelling and Applied Probability.
  32. R.T. Rockafellar, Convex analysis, Princeton Landmarks in Mathematics, Reprint of the 1970 original, Princeton Paperbacks, Princeton University Press (1997) xviii+451.
  33. L. Saloff-Coste, Lectures on finite Markov chains. Lectures on probability theory and statistics (Saint-Flour, 1996). Lect. Notes Math. 1665 (1997) 301–413. [CrossRef]
  34. B. Ycart, A characteristic property of linear growth birth and death processes. The Indian J. Statist. Ser. A 50 (1988) 184–189.
  35. L. Wu, A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields 118 (2000) 427–438. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.