Probability Theory pp 495-504 | Cite as

# Law of the Iterated Logarithm

Chapter

For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large *n* ∈ ℕ, the typical behaviour, or average value behaviour, of sums of *n* random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.

## Keywords

Brownian Motion Central Limit Theorem Iterate Logarithm Real Random Variable Binary Splitting
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer-Verlag London Limited 2008