An exceptional max-stable process fully parameterized by its extremal coefficients

摘要: The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number independent random variables among collection $\{X_t\}_{t\in A}$. We introduce class Tawn-Molchanov processes that is in 1:1 correspondence with ECFs, thus also proving complete characterization ECF terms negative definiteness. corresponding turns out be exceptional all sharing same its dependency maximal w.r.t. inclusion. This entails sharp lower bounds for dimensional distributions arbitrary ECF. A spectral representation and stochastic continuity are discussed. show how build new valid ECFs from given by means Bernstein functions.