32 citations · 39 across the 8 of their papers we have counts for
12 papers
Kernel estimation of the transition density in bifurcating Markov chains
S. Valère Bitseki Penda
We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and a…
Central limit theorem for bifurcating Markov chains: the mother-daughters triangles case
S. Valère Bitseki Penda
The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit th…
Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains models
S. Valère Bitseki Penda
Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by p…
Central limit theorem for bifurcating Markov chains under -ergodic conditions
S. Valère Bitseki Penda, Jean-François Delmas
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We…
Central limit theorem for bifurcating Markov chains under point-wise ergodic conditions
S. Valère Bitseki Penda, Jean-François Delmas
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We…
A phase transition for large values of bifurcating autoregressive models
Vincent Bansaye, S. Valère Bitseki Penda
We describe the asymptotic behavior of the number of individuals with a large value in a stable bifurcating autoregressive process. The study of the associated fi…
Adaptive estimation for bifurcating Markov chains
S. Valère Bitseki Penda, Marc Hoffmann, Adélaïde Olivier
In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and…
Autoregressive Functions Estimation in Nonlinear Bifurcating Autoregressive Models
Siméon Valère Bitseki Penda, Adélaïde Olivier
Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last dec…
Transportation cost-information and concentration inequalities for bifurcating Markov chains
Siméon Valère Bitseki Penda, Mikael Escobar-Bach, Arnaud Guillin
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…
Deviation inequalities for bifurcating Markov chains on Galton-Watson tree
Siméon Valère Bitseki Penda
We provide deviation inequalities for properly normalized sums of bifurcating Markov chains on Galton-Watson tree. These processes are extension of bifurcating Markov chains (which…
Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process
S. Valère Bitseki Penda, Hacène Djellout, Frédéric Proïa
The purpose of this paper is to investigate moderate deviations for the Durbin-Watson statistic associated with the stable first-order autoregressive process where the driven noise…
Deviation inequalities, Moderate deviations and some limit theorems for bifurcating Markov chains with application
Valère Bitseki Penda, Hacène Djellout, Arnaud Guillin
First, under a geometric ergodicity assumption, we provide some limit theorems and some probability inequalities for the bifurcating Markov chains (BMC). The BMC model was introduc…