Deviation inequalities, moderate deviations and some limit theorems for bifurcating Markov chains with application

DOI10.1214/13-AAP921zbMath1293.60036arXiv1111.7303OpenAlexW1965053642MaRDI QIDQ2443192

S. Valère Bitseki Penda, Hacène Djellout, Arnaud Guillin

Publication date: 4 April 2014

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.7303

zbMATH Keywords

ergodicitymartingalemoderate deviationlimit theoremsdeviation inequalitiesbifurcating Markov chainscellular agingfirst-order bifurcating autoregressive process

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Applications of statistics to biology and medical sciences; meta analysis (62P10) Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Markov processes: estimation; hidden Markov models (62M05) Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Large deviations (60F10) Markov processes: hypothesis testing (62M02)

Related Items (16)

Nonparametric estimation of the division rate of an age dependent branching process ⋮ Moderate deviations of functional of Markov Processes ⋮ Central limit theorem for bifurcating markov chains under L²-ergodic conditions ⋮ Equivalent properties for the bifurcating Markov chains indexed by a binary tree ⋮ A phase transition for large values of bifurcating autoregressive models ⋮ Autoregressive functions estimation in nonlinear bifurcating autoregressive models ⋮ Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models ⋮ Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains ⋮ Moderate deviation principles for bifurcating Markov chains: case of functions dependent of one variable ⋮ The asymptotic behaviors for least square estimation of multi-casting autoregressive processes ⋮ Deviation inequalities for bifurcating Markov chains on Galton−Watson tree ⋮ Statistical estimation in a randomly structured branching population ⋮ Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model ⋮ A Central Limit Theorem for punctuated equilibrium ⋮ Central limit theorem for bifurcating Markov chains under pointwise ergodic conditions ⋮ Exponential Growth of Bifurcating Processes with Ancestral Dependence

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