Moderate deviations for stationary sequences of bounded random variables

2007/11/25 by Dedecker, Jérôme, Merlevède, Florence, Peligrad, Magda +1
#60F10 #60G10 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0711.3924

Abstract

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of ϕ-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.

Related

• A Bernstein type inequality and moderate deviations for weakly dependent sequences
• Large and moderate deviations for bounded functions of slowly mixing markov chains
• Moderate deviation principles for bifurcating Markov chains: case of functions dependent of one variable
• Moderate deviations for diffusions with Brownian potentials
• Some examples of non-central moderate deviations for sequences of real random variables