Open Access
November 2017 Transportation and concentration inequalities for bifurcating Markov chains
S. Valère Bitseki Penda, Mikael Escobar-Bach, Arnaud Guillin
Bernoulli 23(4B): 3213-3242 (November 2017). DOI: 10.3150/16-BEJ843


We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful concentration inequalities. We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive function.


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S. Valère Bitseki Penda. Mikael Escobar-Bach. Arnaud Guillin. "Transportation and concentration inequalities for bifurcating Markov chains." Bernoulli 23 (4B) 3213 - 3242, November 2017.


Received: 1 September 2015; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778285
MathSciNet: MR3654805
Digital Object Identifier: 10.3150/16-BEJ843

Keywords: Bifurcating Markov chains , Deviation inequalities , geometric ergodicity , Transportation inequalities , Wasserstein distance

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 4B • November 2017
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