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Exact convergence rate for the maximum of standardized Gaussian increments. (English) Zbl 1189.60063

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.

MSC:

60F15 Strong limit theorems
60F05 Central limit and other weak theorems

Citations:

Zbl 0809.60036

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