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Concentration inequalities and limit theorems for randomized sums
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  • Published: 24 April 2006

Concentration inequalities and limit theorems for randomized sums

  • Sergey G. Bobkov1 &
  • Friedrich Götze2 

Probability Theory and Related Fields volume 137, pages 49–81 (2007)Cite this article

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Abstract.

Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St., S.E, Minneapolis, MN, 55455, USA

    Sergey G. Bobkov

  2. Department of Mathematics, Bielefeld University, Bielefeld, 33501, Germany

    Friedrich Götze

Authors
  1. Sergey G. Bobkov
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  2. Friedrich Götze
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Corresponding author

Correspondence to Sergey G. Bobkov.

Additional information

Research supported in part by NSF Gr. No. 0405587

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Cite this article

Bobkov, S., Götze, F. Concentration inequalities and limit theorems for randomized sums. Probab. Theory Relat. Fields 137, 49–81 (2007). https://doi.org/10.1007/s00440-006-0500-9

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  • Received: 25 June 2005

  • Revised: 18 December 2005

  • Published: 24 April 2006

  • Issue Date: January 2007

  • DOI: https://doi.org/10.1007/s00440-006-0500-9

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Key words or phrases

  • Concentration
  • typical distributions
  • central limit theorem
  • selfnormalized statistics
  • orthogonal polynomials
  • pairwise independent random variables
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