Editing Law of the iterated logarithm (section)

{{Short description|Mathematical theorem}}
[[File:Law of large numbers.gif|thumb|Plot of <math>S_n/n</math> (red), its standard deviation <math>1/\sqrt{n}</math> (blue) and its bound <math>\sqrt{2\log\log n/n}</math> given by LIL (green). Notice the way it randomly switches from the upper bound to the lower bound. Both axes are non-linearly transformed (as explained in figure summary) to make this effect more visible.]]

In [[probability theory]], the '''law of the iterated logarithm''' describes the magnitude of the fluctuations of a [[random walk]]. The original statement of the law of the iterated logarithm is due to [[Aleksandr Khinchin|A. Ya. Khinchin]] (1924).<ref>[[Aleksandr Khinchin|A. Khinchine]]. "Über einen Satz der Wahrscheinlichkeitsrechnung", ''[[Fundamenta Mathematicae]]'' 6 (1924): pp. 9–20 ''(The author's name is shown here in an alternate transliteration.)''</ref> Another statement was given by [[Andrey Kolmogorov|A. N. Kolmogorov]] in 1929.<ref name="Kolmogorov1929">[[Andrey Kolmogorov|A. Kolmogoroff]]. [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN235181684_0101 "Über das Gesetz des iterierten Logarithmus"]. ''Mathematische Annalen'', 101: 126–135, 1929.</ref>