Maxima and Minima and Extremal Theory for Dependent Processes

Abstract

Trivially, extremes in two or more mutually independent processes are independent. In this chapter we shall establish the perhaps somewhat surprising fact that, asymptotically, independence of extremes holds for normal processes even when they are highly correlated. However, we shall first consider the asymptotic independence of maxima and minima in one normal process. Since minima of ξ(t) are maxima for — ξ(t), this can in fact be regarded as a special case of independence between extremes in two processes, namely between the maxima in the completely dependent processes ξ(t)and-ξ(t).