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Moment bounds for dependent sequences in smooth Banach spaces

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  • Dedecker, J.
  • Merlevède, F.

Abstract

We prove a Marcinkiewicz–Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of {T,T2,⋯,Tn}, on a class of smooth functions, when T belongs to a class of nonuniformly expanding maps of the unit interval.

Suggested Citation

  • Dedecker, J. & Merlevède, F., 2015. "Moment bounds for dependent sequences in smooth Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3401-3429.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:9:p:3401-3429
    DOI: 10.1016/j.spa.2015.05.002
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    References listed on IDEAS

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    1. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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    Cited by:

    1. Lin, Han-Mai & Merlevède, Florence, 2022. "On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 198-220.

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