Kolmogorov's law of the iterated logarithm
GPTKB entity
Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:probability_theory
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| gptkbp:appliesTo |
independent and identically distributed random variables
|
| gptkbp:describes |
asymptotic behavior of sums of independent random variables
|
| gptkbp:field |
gptkb:probability_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kolmogorov's law of the iterated logarithm
|
| gptkbp:namedAfter |
gptkb:Andrey_Kolmogorov
|
| gptkbp:publishedIn |
1929
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| gptkbp:relatedTo |
gptkb:Chung's_law_of_the_iterated_logarithm
gptkb:strong_law_of_large_numbers gptkb:central_limit_theorem |
| gptkbp:sentence |
For a sequence of i.i.d. random variables with mean 0 and variance 1, the partial sums S_n satisfy limsup S_n/(sqrt(2n log log n)) = 1 almost surely.
|
| gptkbp:bfsParent |
gptkb:Andrey_Kolmogorov
gptkb:Andrei_Kolmogorov |
| gptkbp:bfsLayer |
5
|