Abstract
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.
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