The Limit Law of the Iterated Logarithm

Xia Chen ()
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Xia Chen: University of Tennessee

Journal of Theoretical Probability, 2015, vol. 28, issue 2, 721-725

Abstract: Abstract For the partial sum $$\{S_n\}$$ of an i.i.d. sequence with zero mean and unit variance, it is pointed out that $$\begin{aligned} \lim _{n\rightarrow \infty }(2\log \log n)^{-1/2}\max _{1\le k\le n}{S_k\over \sqrt{k}} =1\quad \mathrm{{a.s}}. \end{aligned}$$

Keywords: The limit law of the iterated logarithm; Brownian motion; Ornstein–Uhlenbeck process; 60F15; 60G10; 60G15; 60G50 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0481-4

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