Contributions to Books:
A. Jüngel, W. Yue:
"Discrete Beckner inequalities via the bochner-Bakry-Emery approach for Markov chains";
in: "ASC Report 36/2015",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Discrete Beckner inequalities, which interpolate between the modiﬁed loga-rithmic Sobolev inequality and the Poincare´ inequality, are derived for time-continuous Markov chains on countable state spaces. The proof is based on the Bakry-Emery ap-proach and on discrete Bochner-type inequalities established by Caputo, Dai Pra, and Posta and recently extended by Fathi and Maas. The abstract result is applied to several Markov chains, including birth-death processes, zero-range processes, Bernoulli-Laplace models, and random transportation models, and to a ﬁnite-volume discretization of a one-dimensional Fokker-Planck equation, applying results by Mielke.
Time-continuous Markov chain, functional inequality, entropy decay, discrete, Time-continuous Markov chain, functional inequality, entropy decay
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.