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A remark on almost sure convergence of weighted sums
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  • Published: July 1987

A remark on almost sure convergence of weighted sums

  • Rolf Thrum1 

Probability Theory and Related Fields volume 75, pages 425–430 (1987)Cite this article

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Summary

As a generalization of a theorem of Chow [1] it is shown by an elementary method that for i.i.d. r.v.'s X 1,...,X n, with expectation zero and finite p-th absolute moment (p≧2) the weighted sums \(\sum\limits_{i = 1}^n {a_{n,i} X_i /n^{1/p} (\sum\limits_{i = 1}^n {a_{n,i}^2 } } )^{1/2} \) converge to zero a.s.

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References

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  9. Thrum, R.: Uniform almost sure convergence of Weighted sums and applications in regression models. Paper at the 5-th Pannonian Symposium on Mathematical Statistics. May 20–24, 1985, Visegrád, Hungary (1985)

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Authors and Affiliations

  1. Department of Statistics, Humboldt-University at Berlin, Unter den Linden 6, DDR-1086, Berlin, German Democratic Republic

    Rolf Thrum

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  1. Rolf Thrum
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Thrum, R. A remark on almost sure convergence of weighted sums. Probab. Th. Rel. Fields 75, 425–430 (1987). https://doi.org/10.1007/BF00318709

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  • Received: 20 February 1984

  • Issue Date: July 1987

  • DOI: https://doi.org/10.1007/BF00318709

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Absolute Moment
  • Expectation Zero
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