On the extremal behavior of a nonstationary normal random field

Let X={Xn}n⩾1 be a nonstationary random field satisfying a long range weak dependence for each coordinate at a time and a local dependence condition that avoids clustering of exceedances of high values. For these random fields, the probability of no exceedances of high values can be approximated by exp(−τ), where τ is the limiting mean number of exceedances. We present a class of nonstationary normal random fields for which this result can be applied.