Moderate deviations of functional of Markov Processes

Valère Bitseki Penda (1) , Hacène Djellout (1) , Laure Dumaz (2, 3) , Florence Merlevède (4) , Frédéric Proïa (5, 6)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 ENS-PSL - École normale supérieure - Paris
4 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
5 IMB - Institut de Mathématiques de Bordeaux
6 ALEA - Advanced Learning Evolutionary Algorithms

This paper presents recent developments on the principle of moderate deviations for some classes of dependent random variables. This paper groups the contributions of the speakers of the session dedicated to moderate deviations of functional of Markov processes organized during the Journées MAS, which took place in Clermont-Ferrand in August 2012.

Mots clés: Moderate deviations; Markov processes; Martingale approximations; stationary processes; Linear process; strong mixing sequences; Durbin-Watson statistic; autoregressive process; least squares estimator; Bifurcating Markov Chains; true self-repelling motion

Domaines: Probabilités [math.PR]

Valère Bitseki Penda, Hacène Djellout, Laure Dumaz, Florence Merlevède, Frédéric Proïa. Moderate deviations of functional of Markov Processes. ESAIM: Proceedings, 2014, 44, p. 214. ⟨hal-00872322⟩