Harmonizable Processes: Structure.
CALIFORNIA UNIV RIVERSIDE DEPT OF MATHEMATICS
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A unified and detailed treatment of the structure of harmonizable time series is considered. These are divided into strong or Loeve and weak Bochner-Rozanov classes and their characterizations as well as integral representations are obtained. Both concrete and operator versions of the characterizations of weakly harmonizable processes are given. The work here implies that weakly harmonizable class is the largest family of second order processes with continuous covariance for which Fourier analysis applies. The treatment includes random fields. It is shown that both the harmonizable processes have an associated spectrum, and they obey the weak law of large numbers. Multidimensional extensions and filtering are briefly discussed. Several open problems and avenues of research growing out of this study are indicated at various places, so that the material presented here will form a firm basis for both the theory and applications to follow. Author
- Statistics and Probability