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Comparison of moments for tangent sequences of random variables
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  • Published: June 1988

Comparison of moments for tangent sequences of random variables

  • Pawel Hitczenko1 

Probability Theory and Related Fields volume 78, pages 223–230 (1988)Cite this article

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Summary

It is shown that for all tangent sequences (d n) and (e n) of nonnegative or conditionally symmetric random variables and for every function Φ satisfying the growth condition Φ(2x)≦αΦ(x) the following inequality holds: \(E\Phi \left( {\mathop {\sup }\limits_n \left| {\sum\limits_{k = 1}^n {d_k } } \right|} \right) \leqq cE\Phi \left( {\mathop {\sup }\limits_n \left| {\sum\limits_{k = 1}^n {e_k } } \right|} \right)\). This generalizes results of J. Zinn and proves a conjecture of S. Kwapień and W.A. Woyczyński.

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References

  1. Burkholder, D.L.: Distribution function inequalities for martingales. Ann. Probab. 1, 19–42 (1973)

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  2. Kwapień, S., Woyczyński, W.A.: Semimartingale integrals via decoupling inequalities and tangent processes. Case Western Reserve University, preprint, (1986)

  3. McConnell, T., Taqqu, M.: Double integration with respect to symmetric stable processes. Preprint

  4. Seminar notes on multiple stochastic integration, polynomial chaos and their applications. Case Western Reserve University, preprint (1985)

  5. Zinn, J.: Comparison of martingale difference sequences. In: Beck, A., Dudley, R., Hahn, M., Kuelbs, J., Marcus, M. (eds.). Probability in Banach spaces V. (Lect. Notes Math., vol. 1153, pp. 453–457). Berlin Heidelberg New York: Springer 1985

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Authors and Affiliations

  1. Department of Statistics, Academy of Physical Education, Warsaw, Poland

    Pawel Hitczenko

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  1. Pawel Hitczenko
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Hitczenko, P. Comparison of moments for tangent sequences of random variables. Probab. Th. Rel. Fields 78, 223–230 (1988). https://doi.org/10.1007/BF00322019

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  • Received: 03 November 1986

  • Revised: 09 December 1987

  • Issue Date: June 1988

  • DOI: https://doi.org/10.1007/BF00322019

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Keywords

  • Growth Condition
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Zinn
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