Functional limit theorems for maxima in Hölder spaces
نویسنده
چکیده
We establish limit theorems for component–wise maxima of independent and identically distributed heavy–tailed processes. The focus here is on weak convergence in Hölder spaces. Given that the finite–dimensional distributions converge, the classical tightness conditions of Lamperti apply, provided that one can control the tail–behavior of Hölder norms. Here, by using a powerful isomorphism theorem due to Ciesielski, we provide estimates for the tails of Hölder norms for light, moderate and heavy–tailed processes. As a consequence, we establish sufficient conditions for the Hölder regularity of several classes of doubly stochastic max–stable processes such as Schlather and Brown–Resnick processes. Some of our results extend to the case of weak convergence in Besov spaces.
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تاریخ انتشار 2011