Admissible Translates of Stable Processes: A Survey and Some New Models

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1988
Accession Number
ADA200636

Entities

People

  • Stamatis Cambanis

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Contrast
  • Covariance
  • Data Science
  • Detection
  • Gaussian Processes
  • Information Science
  • North Carolina
  • Probability
  • Random Variables
  • Signal Detection
  • Stationary
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • Surveys
  • Universities

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.