Admissible Translates of Stable Processes: A Survey and Some New Models
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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This document surveys some recent results on the admissible translates of stable processes and we contrast them with the analogs for Gaussian processes. Whereas Gaussian moving averages and Fourier transforms of independent increment increments processes have rich classes of admissible translates, their stable counterparts frequently have all translates singular. By removing the requirement of independence of the increments, we introduce stable processes that are generalized moving averages and harmonizable which can have rich classes of admissible translates. These are generally nonstationary processes but we also show a class of stationary generalized moving averages.
- Statistics and Probability