Extremes of quasi-independent random fields and clustering of high values

摘要

Random fields on (Z_+)~d, with long range weak dependence for each coordinate at a time and local restrictions on clustering of high values, behave like an i.i.d. random field. Then, 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. An example is a nonstationary Gaussian field under a Berman's type condition on their correlations. Random fields usually present clustering of high values. Under smooth oscillation conditions, we compute the clustering measure extremal index, from the limiting mean number of crossings of high levels.