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On the best constant in Marcinkiewicz-Zygmund inequality

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  • Ren, Yao-Feng
  • Liang, Han-Ying

Abstract

Let {Xn,n[greater-or-equal, slanted]1} be a sequence of independent r.v.'s with EXn=0, C(p) be the best constant in the following Marcinkiewicz-Zygmund inequality:In this paper we prove that [C(p)]1/p grows like as p-->[infinity] and give an estimate .

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:3:p:227-233
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    Cited by:

    1. Ren, Yao-Feng & Tian, Fan-Ji, 2003. "On the Rosenthal's inequality for locally square integrable martingales," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 107-116, March.
    2. Ramazan Kadiev & Arcady Ponosov, 2018. "Lyapunov Stability of the Generalized Stochastic Pantograph Equation," Journal of Mathematics, Hindawi, vol. 2018, pages 1-9, June.
    3. Ferger, Dietmar, 2014. "Optimal constants in the Marcinkiewicz–Zygmund inequalities," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 96-101.
    4. Crisan, D. & Li, K., 2015. "Generalised particle filters with Gaussian mixtures," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2643-2673.
    5. Cloez, Bertrand & Corujo, Josué, 2022. "Uniform in time propagation of chaos for a Moran model," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 251-285.
    6. 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.
    7. Li, Bainian & Zhang, Kongsheng & Wu, Libin, 2011. "A sharp inequality for martingales and its applications," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1260-1266, August.

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