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 $n\in \mathbb{N}$the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.
CITATION STYLE
Klenke, A. (2014). Law of the Iterated Logarithm (pp. 509–519). https://doi.org/10.1007/978-1-4471-5361-0_22
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