Harmonizable Stable Processes on Groups: Spectral, Ergodic and Interpolation Properties.

Abstract

This work extends to symmetric alpha-stable (S alpha S) processes, 1 < alpha < 2, which are Fourier transforms of independently scattered random measures on locally compact Abelian groups, some of the basic results known for processes with finite second moments and for Gaussian processes. Analytic conditions for subordination of left (right) stationarily related processes and a weak law of large numbers are obtained. The main results deal with the interpolation problem. Characterization of minimal and interpolable processes on discrete groups are derived. Also formulas for the interpolator and the corresponding interpolation error are given. This yields a solution of the interpolation problem for the considered class of stable processes in this general setting. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1983
Accession Number
ADA136504

Entities

People

  • A. Weron

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Complex Numbers
  • Data Science
  • Fourier Analysis
  • Gaussian Processes
  • Information Science
  • Integrals
  • Interpolation
  • North Carolina
  • Numbers
  • Probability
  • Random Variables
  • Sequences
  • Stationary Processes
  • Statistics
  • Stochastic Processes
  • Walsh Functions

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.