We have found the limit ℒh = lim inf (log2 T)2/3 T → ∞ ∥W(T·)/(2T log2 T)1/2 - h∥ for a Wiener process W and a class of twice weakly differentiable functions h ∈ C[0, 1], thus solving the problem of the convergence rate in Chung's functional law for the so-called "slowest points". Our description is closely related to an interesting functional emerging from a large deviation problem for the Wiener process in a strip.
Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty