Transportation and concentration inequalities for bifurcating Markov chains

Abstract : 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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Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 5 septembre 2017 - 16:24:28
Dernière modification le : jeudi 21 juin 2018 - 01:09:51



Siméon Valère Bitseki Penda, Mikael Escobar-Bach, Arnaud Guillin. Transportation and concentration inequalities for bifurcating Markov chains. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (4B), pp.3213 - 3242. ⟨10.3150/16-BEJ843⟩. ⟨hal-01582161⟩



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