Extremes of Continuous Parameter Stationary Processes

Abstract

Our primary task in this chapter will be to discuss continuous parameter analogues of the sequence results of Chapter 3, and, in particular, to obtain a corresponding version of the Extremal Types Theorem which applies in the continuous parameter case. This will be taken up in the first section, using a continuous parameter analogue of the dependence restriction D(u_n). Limits for probabilities P{M(T) ≤ u_T} are then considered for arbitrary families of constants {u_T}, leading, in particular, to a determination of domains of attraction.