ON THE LINK BETWEEN DEPENDENCE AND INDEPENDENCE IN EXTREME VALUE THEORY FOR DYNAMICAL SYSTEMS

Abstract. It is well known that under some conditions on the dependence structure we can relate the asymptotic distribution of the partial maximum of a stationary stochastic process with the maximum of an associated independent sequence of random variables with the same distribution function of the dependent one. These conditions are known as D(un) and D′(un). Although D(un) is of mixing type, when studying stochastic processes arising from a dynamical system with good mixing properties, verifying D(un) is not straightforward. We propose a reformulation of D(un) so that its validity may follow easily if we have a certain decay of correlations for the dynamical system in consideration. 1