Transportation cost-information and concentration inequalities for bifurcating Markov chains

Abstract

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.

References in corpus (5)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
• A characterization of dimension free concentration in terms of transportation inequalities
• Deviation inequalities, Moderate deviations and some limit theorems for bifurcating Markov chains with application
• Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

Cited by in corpus (1)

• Autoregressive Functions Estimation in Nonlinear Bifurcating Autoregressive Models