Ergodic Properties of Stationary Stable Processes.

Abstract

Spectral necessary and sufficient conditions are derived for stationary symmetric stable processes to be metrically transitive and mixing. Then consider some important classes of stationary stable processes: Sub-Gaussian stationary processes and stationary stable processes with a harmonic spectral representation are never metrically transitive, the latter in sharp contrast with the Gaussian case. Stable processes with a harmonic spectral representation satisfy a strong law of large numbers even though they are not generally stationary. For doubly stationary stable processes, sufficient conditions are derived for metric transitivity and mixing, and necessary and sufficient conditions for a strong law of large numbers.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA185281

Entities

People

  • Aleksander Weron
  • Clyde D. Hardin Jr.
  • Stamatis Cambanis

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Contrast
  • Convergence
  • Data Science
  • Differential Equations
  • Gaussian Processes
  • Guarantees
  • Inequalities
  • Information Science
  • Probability
  • Random Variables
  • Stationary
  • Stationary Processes
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • Universities

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Mathematical Modeling and Probability Theory.