ON EXTREMAL INDEX OF MAX-STABLE STATIONARY PROCESSES

In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process W(t); t is an element of R, as H-W(delta) = lim(T ->infinity) T-1E{sup(t is an element of delta Z boolean AND[0;T]) e(W(t))}, delta >= 0 (set 0Z = R if delta = 0) and the extremal index of the associated max-stable stationary process xi W. We derive several new formulas and obtain lower bounds for H-W(delta) if W is a Gaussian or a Levy process. As a by-product we show an interesting relation between Pickands constants and lower tail probabilities for fractional Brownian motions.