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Almost certain behavior of row sums of double arrays

  • Henry Teicher
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)

Abstract

The almost certain (probability one) behavior of row sums Open image in new window of double arrays of rowwise independent random variables Xn, i is investigated primarily when the Xn, i assume only the values zero and one. If knpn, the expected number of successes, grows more rapidly than C log n, then Open image in new window converges almost certainly to one. However, when the expected number of successes grows less rapidly than C log n, it no longer determines the asymptotic behavior of Open image in new window and the outcome depends upon additional stochastic assumptions. Two alternative sets of stochastic constraints are imposed and the behavior of Open image in new window under each is analyzed and contrasted. Finally, the case of exponential random variables is considered briefly.

Keywords

Triangular Array Independent Column Poisson Probability Standard Normal Density Poisson Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Rosalsky, A. and Teicher, H., A limit theorem for double arrays. Ann. Prob. 9 (1981).Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Henry Teicher
    • 1
  1. 1.Department of StatisticsRutgers UniversityNew BrunswickUSA

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