Deviation inequalities for bifurcating Markov chains on Galton-Watson tree

Siméon Valère Bitseki Penda (1)

1 Probabilité, Analyse et Statistique

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 was introduced by Guyon to detect cellular aging from cell lineage) in case the index set is a binary Galton-Watson process. As application, we derive deviation inequalities for the least-squares estimator of autoregressive parameters of bifurcating autoregressive processes with missing data. These processes allow, in case of cell division, to take into account the cell's death. The results are obtained under an uniform geometric ergodicity assumption of an embedded Markov chain.

Mots clés: Bifurcating Markov chains; Galton-Watson processes; ergodicity; deviation inequalities; first order bifurcating autoregressive process with missing data; cellular aging

Domaines: Probabilités [math.PR]

Siméon Valère Bitseki Penda. Deviation inequalities for bifurcating Markov chains on Galton-Watson tree. 2013. ⟨hal-00789557⟩