Mathematics – Probability
Scientific paper
2011-11-30
Mathematics
Probability
44 pages
Scientific paper
Firstly, under geometric ergodicity assumption, we provide some limit theorems and some probability inequalities for bifurcating Markov chains introduced by Guyon to detect cellular aging from cell lineage, thus completing the work of Guyon. This probability inequalities are then applied to derive a first result on moderate deviation principle for a functional of bifurcating Markov chains with a restricted range of speed, but with a function which can be unbounded. Next, under uniform geometric ergodicity assumption, we provide deviation inequalities for bifurcating Markov chains and apply them to derive a second result on moderate deviation principle for bounded functional of bifurcating Markov chains with a more larger range of speed. As statistical applications, we provide superexponential convergence in probability and deviation inequalities (under the gaussian setting or the bounded setting), and moderate deviation principle for least square estimators of the parameters of a first order bifurcating autoregressive process.
Djellout Hacène
Guillin Arnaud
Penda Valère Bitseki
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