Transportation cost-information and concentration inequalities for bifurcating Markov chains

Transportation cost-information and concentration inequalities for bifurcating Markov chains

We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives birth to two offsprings in the next one. Transportation cos...

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Veröffentlicht in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2017-10, Vol.23 (4B), p.3213-3242
Hauptverfasser: Bitseki Penda, Siméon Valère, Escobar-Bach, Mikael, Guillin, Arnaud
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container_issue 4B
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container_title Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
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creator Bitseki Penda, Siméon Valère
Escobar-Bach, Mikael
Guillin, Arnaud
description We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives birth to two offsprings in the next one. Transportation cost inequalities provide useful concentra-tion inequalities. We also study deviation inequalities for the empiri-cal means under relaxed assumptions on the Wasserstein contraction of the Markov kernels. Applications to bifurcating non linear autore-gressive processes are considered: deviation inequalities for pointwise estimates of the non linear leading functions.
doi_str_mv 10.3150/16-BEJ843
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source Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics
subjects Mathematics
Probability
Statistics
title Transportation cost-information and concentration inequalities for bifurcating Markov chains
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