## Bernoulli

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

### 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.

#### Article information

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

Dates
First available in Project Euclid: 23 May 2017

https://projecteuclid.org/euclid.bj/1495505091

Digital Object Identifier
doi:10.3150/16-BEJ843

Mathematical Reviews number (MathSciNet)
MR3654805

Zentralblatt MATH identifier
06778285

#### Citation

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. https://projecteuclid.org/euclid.bj/1495505091

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