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Etude statistique de séquences biologiques et convergence de martingales

Abstract : The Chaos Game Representation is a dynamical system
which maps a sequence of letters taken from a finite alphabet onto an empirical measure on a set. We show how the CGR can be used to
characterize the
order of an homogeneous Markov chain and to define a new family of tests.
Then we propose a construction of Digital Search Trees, inspired
from the CGR, by successively inserting all the returned prefixes of a Markov
chain. We give the asymptotic behavior of the critical lengths of paths, which
turns out to be, at first order, the same one as in the case of DST built from
independent Markov chains.
A last part deals with properties of almost sure convergence of vectorial
martingales. Under suitable regularity conditions on the
growing process, we establish the convergence of normalized moments of all
orders in the almost sure central limit theorem. The results are
applied to the cumulated errors of estimation and
prediction in linear regression models and branching processes.
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Contributor : Peggy Cenac <>
Submitted on : Thursday, March 1, 2007 - 3:44:10 PM
Last modification on : Friday, April 10, 2020 - 5:20:17 PM
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  • HAL Id : tel-00134328, version 1


Peggy Cenac. Etude statistique de séquences biologiques et convergence de martingales. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2006. Français. ⟨tel-00134328⟩



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