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Exact Convergence Rate for the Maximum of Standardized Gaussian Increments

   
@article{ECP1380,
	author = {Zakhar Kabluchko and Axel Munk},
	title = {Exact Convergence Rate for the Maximum of Standardized Gaussian Increments},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {standardized increments, gaussian random walk, multiscale statistic, L'evy's continuity modulus, integral test, almost sure limit theorem},
	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.},
	pages = {no. 30, 302-310},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1380},    
        url = {http://ecp.ejpecp.org/article/view/1380}}