On the weak law of large numbers and the generalized elementary renewal theorem

@article{Smith1967OnTW,
  title={On the weak law of large numbers and the generalized elementary renewal theorem},
  author={W. L. Smith},
  journal={Pacific Journal of Mathematics},
  year={1967},
  volume={22},
  pages={171-188}
}
  • W. L. Smith
  • Published 1967
  • Mathematics
  • Pacific Journal of Mathematics
    • SUMMARY Much use is made of the fact that a necessary and sufficient condition for A Generalized Elementary Renewal Theorem (GERT) gives conditions such that, in which case (ex l + ",+ (~Xn)/n necessarily tends to J..L as n-> 00 , Finally, an example shows that (*) can hold while the WLLN fails to hold. 
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    6 Citations
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    • 5
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    • 2
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    • 10
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    • 4
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    References

    SHOWING 1-4 OF 4 REFERENCES
    On the relative stability of sums of positive random variables
    • 2
    • Highly Influential
    On the elementary renewal theorem for non-identically distributed variables
    • 29
    • PDF
    Limit Distributions for Sums of Independent Random Variables
    • 1,882
    and A
    • N. Kolmogorov, Limit distributions for sums of Independent Random Variables, Addison-Wesley, Cambridge, Mass.,
    • 1954