Accession Number : ADA186426

Title :   Admissible and Singular Translates of Stable Processes.

Descriptive Note : Technical rept. Sep 86-Aug 87,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Marques, Mauro ; Cambanis, Stamatis

PDF Url : ADA186426

Report Date : Aug 1987

Pagination or Media Count : 43

Abstract : Translates of symmetric stable and other p sub th order processes are considered. An upper bound for the set of admissible translates of a general p sub th order process is presented, which is a partial analog of the reproducing kernel Hilbert space of a second order process. For invertible stable processes a dichotomy is established, i.e. each translate is either admissible or singular, and the admissible translates are characterized. As a consequence, most continuous time moving averages and all harmonizable processes with nonatomic spectral measure have no admissible translate; and the admissible translates of a general harmonizable process are characterized. The translates of a mixed autoregressive moving averages stable sequence are shown to coincide with those of the Gaussian case.

Descriptors :   *FUNCTIONAL ANALYSIS, ANALOG SYSTEMS, HILBERT SPACE, MEAN, MOTION, STABILITY, TIME, KERNEL FUNCTIONS, BANACH SPACE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE