On the Exeedance Random Measures for Stationary Processes.
Abstract
Two common approaches to extremal theory for stationary processes involve (a) consideration of point processes of upcrossings of high levels and (b) use of the total exceedance time above such levels. The approach (a) yields a greater variety of interesting results regarding the global and local maxima, but requires more by way of regularity conditions on the sample paths, than does the approach (b). This work combines both approaches by consideration of the exceedance random measure thereby obtaining general results under weak conditions on the sample functions. These include previously known results in the case where more sample function regularity is assumed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1987
- Accession Number
- ADA192838
Entities
People
- M. Ross Leadbetter
Organizations
- University of North Carolina at Chapel Hill