Abstract
We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized gaussian random walk increments. This gives a more precise version of Shao's theorem (Shao, Q.-M., 1995. On a conjecture of Révész. Proc. Amer. Math. Soc. 123, 575-582) in the gaussian case.
Citation
Zakhar Kabluchko. Axel Munk. "Exact Convergence Rate for the Maximum of Standardized Gaussian Increments." Electron. Commun. Probab. 13 302 - 310, 2008. https://doi.org/10.1214/ECP.v13-1380
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