Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro Caputo; Paolo Dai Pra; Gustavo Posta

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 3, page 734-753
  • ISSN: 0246-0203

Abstract

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We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results were limited to the homogeneous case, and obtained via the martingale approach, whose applicability to inhomogeneous models is still unclear.

How to cite

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Caputo, Pietro, Dai Pra, Paolo, and Posta, Gustavo. "Convex entropy decay via the Bochner–Bakry–Emery approach." Annales de l'I.H.P. Probabilités et statistiques 45.3 (2009): 734-753. <http://eudml.org/doc/78041>.

@article{Caputo2009,
abstract = {We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results were limited to the homogeneous case, and obtained via the martingale approach, whose applicability to inhomogeneous models is still unclear.},
author = {Caputo, Pietro, Dai Pra, Paolo, Posta, Gustavo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {entropy decay; modified logarithmic Sobolev inequality; stochastic particle systems},
language = {eng},
number = {3},
pages = {734-753},
publisher = {Gauthier-Villars},
title = {Convex entropy decay via the Bochner–Bakry–Emery approach},
url = {http://eudml.org/doc/78041},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Caputo, Pietro
AU - Dai Pra, Paolo
AU - Posta, Gustavo
TI - Convex entropy decay via the Bochner–Bakry–Emery approach
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 3
SP - 734
EP - 753
AB - We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results were limited to the homogeneous case, and obtained via the martingale approach, whose applicability to inhomogeneous models is still unclear.
LA - eng
KW - entropy decay; modified logarithmic Sobolev inequality; stochastic particle systems
UR - http://eudml.org/doc/78041
ER -

References

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