A note on upper estimates for Pickands constants

Pickands constants play a significant role in the extreme value theory of Gaussian processes. Recall that where {B[alpha](t),t>=0} is a fractional Brownian motion with Hurst parameter [alpha]/2 and [alpha][set membership, variant](0,2]. In this note we derive new upper bounds for and [alpha][set membership, variant](1,2]. The obtained results improve bounds given by Shao [Shao, Q.M., 1996. Bounds and estimators of a basic constant in extreme value theory of Gaussian processes. Statist. Sinica 6, 245-257].