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Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions

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  • Emmanuel Rio

    (UMR 8100 CNRS—Laboratoire de mathématiques de Versailles)

Abstract

We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in $\mathbb{L}^{p}$ for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am. Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of $\mathbb{L}^{p}$ -norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular Markov chain are given.

Suggested Citation

  • Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:1:d:10.1007_s10959-008-0155-9
    DOI: 10.1007/s10959-008-0155-9
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    References listed on IDEAS

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    1. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
    2. Ren, Yao-Feng & Liang, Han-Ying, 2001. "On the best constant in Marcinkiewicz-Zygmund inequality," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 227-233, June.
    3. Richard C. Bradley, 1997. "On Quantiles and the Central Limit Question for Strongly Mixing Sequences," Journal of Theoretical Probability, Springer, vol. 10(2), pages 507-555, April.
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