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Pré-Publication, Document De Travail Année : 2012

Strong invariance principles with rate for "reverse" martingales and applications

Résumé

In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}\log^\beta n$, $2< p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar conclusions in the context of some non-invertible dynamical systems. For instance we treat several classes of uniformly expanding maps of the interval (for possibly unbounded functions). A general result for $\phi$-dependent sequences is obtained in the course.
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Dates et versions

hal-00745647 , version 1 (26-10-2012)
hal-00745647 , version 2 (13-11-2012)

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  • HAL Id : hal-00745647 , version 1

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Christophe Cuny, Florence Merlevède. Strong invariance principles with rate for "reverse" martingales and applications. 2012. ⟨hal-00745647v1⟩
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