law of the iterated logarithm
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:probability_theory
|
| gptkbp:alsoKnownAs |
gptkb:LIL
|
| gptkbp:appliesTo |
independent and identically distributed random variables
|
| gptkbp:category |
limit theorem
|
| gptkbp:describes |
asymptotic behavior of sums of random variables
|
| gptkbp:field |
gptkb:probability_theory
|
| gptkbp:generalizes |
gptkb:strong_law_of_large_numbers
gptkb:central_limit_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
law of the iterated logarithm
|
| gptkbp:namedAfter |
iterated logarithm
|
| gptkbp:provenBy |
gptkb:A._Ya._Khinchin
gptkb:A._N._Kolmogorov |
| gptkbp:relatedTo |
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:usedIn |
stochastic processes
martingale theory random walks |
| gptkbp:yearProposed |
1924
|
| gptkbp:bfsParent |
gptkb:Chung's_law_of_the_iterated_logarithm
|
| gptkbp:bfsLayer |
7
|