Transportation and concentration inequalities for bifurcating Markov chains. (English) Zbl 1407.60095

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

Bernoulli 23, No. 4B, 3213-3242 (2017).

Summary: 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.

MSC:

60J05	Discrete-time Markov processes on general state spaces
60E15	Inequalities; stochastic orderings
62G07	Density estimation

Keywords:

bifurcating Markov chains; deviation inequalities; geometric ergodicity; transportation inequalities; Wasserstein distance