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2008 Exact Convergence Rate for the Maximum of Standardized Gaussian Increments
Zakhar Kabluchko, Axel Munk
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Electron. Commun. Probab. 13: 302-310 (2008). DOI: 10.1214/ECP.v13-1380


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.


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Zakhar Kabluchko. Axel Munk. "Exact Convergence Rate for the Maximum of Standardized Gaussian Increments." Electron. Commun. Probab. 13 302 - 310, 2008.


Accepted: 17 June 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60063
MathSciNet: MR2415138
Digital Object Identifier: 10.1214/ECP.v13-1380

Primary: 60F15

Keywords: almost sure limit theorem , Gaussian random walk , Integral test , Lévy's continuity modulus , multiscale statistic , standardized increments

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