Transportation cost-information and concentration inequalities for bifurcating Markov chains
Bitseki Penda, Siméon Valère ; Escobar-Bach, Mikael ; Guillin, Arnaud
HAL, hal-01109760 / Harvested from HAL
Text on HAL
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.
Publié le : 2015-01-26
Classification:  geometric ergodicity,  Wasserstein distance,  deviation inequalities,  bi-furcating Markov chains,  Transportation cost-information inequalities,  60J05,60J85,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-01109760,
     author = {Bitseki Penda, Sim\'eon Val\`ere and Escobar-Bach, Mikael and Guillin, Arnaud},
     title = {Transportation cost-information and concentration inequalities for bifurcating Markov chains},
     journal = {HAL},
     volume = {2015},
     number = {0},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01109760}
}

Bitseki Penda, Siméon Valère; Escobar-Bach, Mikael; Guillin, Arnaud. Transportation cost-information and concentration inequalities for bifurcating Markov chains. HAL, Tome 2015 (2015) no. 0, . http://gdmltest.u-ga.fr/item/hal-01109760/