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On the Product of Random Variables and Moments of Sums Under Dependence

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High Dimensional Probability VII

Part of the book series: Progress in Probability ((PRPR,volume 71))

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Abstract

In this paper we compare the moments of products of dependent random vectors with the corresponding ones of independent vectors with the same marginal distributions. Various applications of this result are pointed out, including inequalities for the maximum of dependent random variables and moments of partial sums. The inequalities involve the generalized phi-mixing coefficient.

Mathematics Subject Classification (2010). Primary 60E15; Secondary 60F05

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Acknowledgements

I would like to thank to Wlodek Bryc for useful discussions and to the referees for comments which improved the presentation of this paper.

This research was supported in part by a Charles Phelps Taft Memorial Fund grant and the NSF grant DMS-1512936.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, 210025, Cincinnati, OH, 45221-0025, USA

    Magda Peligrad

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  1. Magda Peligrad
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Correspondence to Magda Peligrad .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, Georgia, USA

    Christian Houdré

  2. University of Delaware, Department of Applied Economics and Stat University of Delaware, Newark, Delaware, USA

    David M. Mason

  3. Centre national de la recherche scientifique, Laboratoire J.A. Dieudonné, Université Côte d’Azur, Nice, France

    Patricia Reynaud-Bouret

  4. Department of Mathematics, University of Tennessee Department of Mathematics, Knoxville, Tennessee, USA

    Jan Rosiński

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Dedicated to the memory of Evarist Giné

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Peligrad, M. (2016). On the Product of Random Variables and Moments of Sums Under Dependence. In: Houdré, C., Mason, D., Reynaud-Bouret, P., Rosiński, J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40519-3_7

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