• Bernoulli
  • Volume 23, Number 4B (2017), 3213-3242.

Transportation and concentration inequalities for bifurcating Markov chains

S. Valère Bitseki Penda, Mikael Escobar-Bach, and Arnaud Guillin

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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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Bernoulli, Volume 23, Number 4B (2017), 3213-3242.

Received: September 2015
First available in Project Euclid: 23 May 2017

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Zentralblatt MATH identifier

bifurcating Markov chains deviation inequalities geometric ergodicity transportation inequalities Wasserstein distance


Bitseki Penda, S. Valère; Escobar-Bach, Mikael; Guillin, Arnaud. Transportation and concentration inequalities for bifurcating Markov chains. Bernoulli 23 (2017), no. 4B, 3213--3242. doi:10.3150/16-BEJ843.

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