Probability, Networks and Algorithms Some remarks on properties of generalized Pickands constants

We study properties of generalized Pickands constants H that appear in the extreme value theory of Gaussian processes and are de ned via the limit H lim T H T T where H T IE exp maxt T p t Var t and t is a centered Gaussian process with stationary increments We give estimates of the rate of convergence of H T T to H and prove that if n t weakly converges in C to t then under some weak conditions limn H n H As an application we prove that HB is continuous on where B t is a fractional Brownian motion with Hurst parameter It contradicts the conjecture that is discontinuous at Mathematics Subject Classi cation G primary G M secondary