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A Hàjek-Rényi extension of Lévy's inequality and some applications

  • P. J. Bickel
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References

  1. [1]
    B. v. Bahr andC. G. Esseen, Inequalities for therth absolute moments of a sum of random variables, 1≦r≦2,Ann. Math. Statist.,36 (1965), pp. 299–303.Google Scholar
  2. [2]
    Y. S. Chow, A martingale inequality and the law of large numbers,Proc. Amer. Math. Soc.,11 (1960), pp. 107–111.Google Scholar
  3. [3]
    Y. S. Chow andH. Robbins, On optimal stopping rules forS n/n,Ill. Journal of Math.,9 (1965), pp. 444–454.Google Scholar
  4. [4]
    J. L. Doob,Stochastic processes, J. Wiley and Sons (New York, 1953).Google Scholar
  5. [5]
    A. Dvoretzky, Existence and properties of certain optimal stopping rules,Proc. Fifth Berk. Symp. VI. (1967).Google Scholar
  6. [6]
    P. Feder, D. Siegmund andG. Simons, Existence of optimal stopping rules for rewards related toS n/n, Submitted toAnn. Math. Statist.Google Scholar
  7. [7]
    J. Hàjek andA. Rényi, Generalization of an inequality of Kolmogoroff,Acta Math. Acad. Sci. Hung.,6 (1955), pp. 281–283.Google Scholar
  8. [8]
    G. H. Hardy, J. Littlewood andG. Pólya,Inequalities (Second Edition, Cambridge University Press, 1952).Google Scholar
  9. [9]
    M. Loève,Probability theory (Second Edition, D. Van Nostrand Company, New York, 1960).Google Scholar
  10. [10]
    J. Marcinkiewicz andA. Zygwund, Sur les fonctions indepéndantes,Fund. Math.,29 (1937), pp. 60–90.Google Scholar
  11. [11]
    H. Teicher, A dominated ergodic type theorem,Z. Warscheinlichkeitstheorie Verw. Geb.,8 (1967), pp. 113–116.Google Scholar
  12. [12]
    H. Teicher andJ. Wolfowitz, Existence of optimal stopping rules for linear and quadratic rewards,Z. Warscheinlichkeitstheorie Verw. Geb.,5 (1966), pp. 316–318.Google Scholar
  13. [13]
    S. Berman, Sign invariant random variables and stochastic processes with sign invariant elements,Trans. Amer. Math. Soc.,119 (1965), pp. 216–240.Google Scholar

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© Akadémiai Kiadó 1970

Authors and Affiliations

  • P. J. Bickel
    • 1
  1. 1.Department of statisticsUniversity of californiaBerkeleyUSA

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