Exact Convergence Rate for the Maximum of Standardized Gaussian Increments

Zakhar Kabluchko (Goettingen University)
Axel Munk (Goettingen University)

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.

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Pages: 302-310

Publication Date: June 17, 2008

DOI: 10.1214/ECP.v13-1380

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