Harmonizable Processes: Structure.

Abstract

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)

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Document Details

Document Type
Technical Report
Publication Date
Nov 05, 1980
Accession Number
ADA093302

Entities

People

  • M. M. Rao

Organizations

  • University of California, Riverside

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Covariance
  • Data Science
  • Filtration
  • Fourier Analysis
  • Hilbert Space
  • Information Science
  • Integrals
  • Measure Theory
  • Probability
  • Random Variables
  • Scalar Functions
  • Stationary
  • Stationary Processes
  • Step Functions
  • Theorems

Readers

  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.