Extremes of space-time Gaussian processes

Let be a space-time Gaussian process which is stationary in the time variable t. We study Mn(h)=supt[set membership, variant][0,n]Zt(snh), the supremum of Z taken over t[set membership, variant][0,n] and rescaled by a properly chosen sequence sn-->0. Under appropriate conditions on Z, we show that for some normalizing sequence bn-->[infinity], the process bn(Mn-bn) converges as n-->[infinity] to a stationary max-stable process of Brown-Resnick type. Using strong approximation, we derive an analogous result for the empirical process.