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Strong Law of Large Numbers

  1. Jun 27, 2005 #1
    For the Strong Law of Large Numbers, as far as I know it applies when, let say, the random variables {Xn: n=1,2,...} are iid, hence uncorrelated, their second moments have a common bound and they have a finite mean mu.
    What else I must consider? Is there anyother consideretion or case when the SLLN does not apply?
     
  2. jcsd
  3. Jun 28, 2005 #2

    mathman

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    There are weaker conditions for the strong law to hold.

    For example, the Kolmogoroff Criterion does not require the distributions be identical.
    It needs sum (Vk/k2) be a convergent series (V=variance).

    Alternatively if the distributions are identical, all you need is the mean - the variance may be infinite.
     
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