Strong mixing properties of max-infinitely divisible random fields

Let η=(η(t))t∈T be a sample continuous max-infinitely random field on a locally compact metric space T. For a closed subset S⊂T, we denote by ηS the restriction of η to S. We consider β(S1,S2), the absolute regularity coefficient between ηS1 and ηS2, where S1,S2 are two disjoint closed subsets of T. Our main result is a simple upper bound for β(S1,S2) involving the exponent measure μ of η: we prove that β(S1,S2)≤2∫P[η≮S1f,η≮S2f]μ(df), where f≮Sg means that there exists s∈S such that f(s)≥g(s).