A Note on the Dependence Conditions for Stationary Normal Sequences

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition D(u(n)) and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper D(u(n)) condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.