MODERATE DEVIATION PRINCIPLES FOR BIFURCATING MARKOV CHAINS: CASE OF FUNCTIONS DEPENDENT OF ONE VARIABLE
| Autor: | Bitseki Penda, Siméon Valère, Gackou, Gorgui |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Bitseki Penda, Siméon Valère |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] 60J80 Bifurcating Markov chains binary trees [MATH]Mathematics [math] binary trees Mathematics Subject Classification (2020): 60F10 deviation inequalities Mathematics - Probability moderate deviation principles |
| Zdroj: | ALEA : Latin American Journal of Probability and Mathematical Statistics ALEA : Latin American Journal of Probability and Mathematical Statistics, 2022, 19 (1), pp.617. ⟨10.30757/ALEA.v19-24⟩ |
| ISSN: | 1980-0436 |
| DOI: | 10.30757/ALEA.v19-24⟩ |
| Popis: | The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be seen as the models which represent the evolution of a trait along a population where each individual has two offsprings. Unlike the previous results of Bitseki, Djellout \& Guillin (2014), we consider here the case of functions which depend only on one variable. So, mainly inspired by the recent works of Bitseki \& Delmas (2020) about the central limit theorem for general additive functionals of bifurcating Markov chains, we give here a moderate deviation principle for additive functionals of bifurcating Markov chains when the functions depend on one variable. This work is done under the uniform geometric ergodicity and the uniform ergodic property based on the second spectral gap assumptions. The proofs of our results are based on martingale decomposition recently developed by Bitseki \& Delmas (2020) and on results of Dembo (1996), Djellout (2001) and Puhalski (1997). Comment: 23 pages, 4 figures |
| Databáze: | OpenAIRE |
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