R. Chernick, Michael et al., Calculating the extremal index for a class of stationary sequences, Advances in applied probability , 23(4), 1991, pp. 835-850
A local mixing condition D(k) is introduced for stationary sequences satisfying Leadbetter's condition D. Under the local mixing condition, the asymptotic distribution of the sample maximum can be calculated with the knowledge of the joint distribution of k consecutive terms. Some examples are given to illustrate the notion.