Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Spectral theory for random closed sets and estimating the covariance via frequency space
 Advances in applied probability 35 (2003), No.3, pp.603613 ISSN: 00018678 

 English 
 Journal Article 
 Fraunhofer ITWM () 
Abstract
A spectral theory for stationary random closed sets is developed and provided with a sound mathematical basis. The definition and a proof of the existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a WienerKhinchin theorem for the power spectrum are used to two ends. First, wellknown secondorder characteristics like the covariance can be estimated faster than usual via frequency space. Second, the Bartlett spectrum and the power spectrum can be used as secondorder characteristics in frequency space. Examples show that in some cases information about the random closed set is easier to obtain from these characteristics in frequency space than from their realworld counterparts.