Extremes of Moving Averages of Stable Processes.
Abstract
In this paper extremes of non-normal stable moving average processes are studied. The extremes are described as a marked point process, consisting of the point process of (separated) exceedances of a level together with marks associated with the points, a mark being the normalized sample path of X(t) around an exceedance. It is proved that this marked point process converges in distribution as the level increases to infinity. The limiting distribution is that of a Poisson process with independent marks which have random heights but otherwise are deterministic. As a byproduct of the proof for the continuous-time case, a result on sample path continuity of stable processes is obtained.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1976
- Accession Number
- ADA032696
Entities
People
- Holger Rootzen
Organizations
- University of North Carolina at Chapel Hill