Kabluchko, Zakhar; Munk, Axel Exact convergence rate for the maximum of standardized Gaussian increments. (English) Zbl 1189.60063 Electron. Commun. Probab. 13, 302-310 (2008). Summary: 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 [Q.-M. Shao, Proc. Am. Math. Soc. 123, No. 2, 575–582 (1995; Zbl 0809.60036)] in the gaussian case. Cited in 9 Documents MSC: 60F15 Strong limit theorems 60F05 Central limit and other weak theorems Keywords:standardized increments; Gaussian random walk; multiscale statistic; Lévy’s continuity modulus; integral test; almost sure limit theorem Citations:Zbl 0809.60036 Software:ftnonpar PDFBibTeX XMLCite \textit{Z. Kabluchko} and \textit{A. Munk}, Electron. Commun. Probab. 13, 302--310 (2008; Zbl 1189.60063) Full Text: DOI EuDML EMIS