Kabluchko, ZakharZakharKabluchkoMunk, AxelAxelMunk2022-06-082022-06-082008https://resolver.sub.uni-goettingen.de/purl?gro-2/110074We prove an almost sure limit theorem on the exact convergence rate of the maximum of standarized gaussian random walk increments. This gives a more precise version of Shao's theorem (Shao, Q.-M., 1995. On a conjecture of Revesz. Proc. Amer. Math. Soc. 123, 575-582) in the gaussian case.enjournal_article10.1214/ECP.v13-13800002568514000013143279