On Stable Markov Processes.

Abstract

Necessary conditions are given for a symmetric alpha-stable (SaS) process, 1<alpha<2, to be Markov. These conditions are then applied to find Markov or weakly Markov processes within certain important classes of S/alpha/S processes: time changed Levy motion, sub-Gaussian processes, moving averages and harmonizable processes. Two stationary S/alpha/ S Markov processes are introduced, the right and the left S/alpha/S Ornstein-Uhlenbeck processes. Some of the results are in sharp contrast to the Gaussian case alpha=2. Keywords: Harmonizable process; Stable conditional distribution.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1987
Accession Number
ADA192892

Entities

People

  • Gennady Samorodnitsky
  • Robert J. Adler
  • Stamatis Gambanis

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Brownian Motion
  • Classification
  • Contrast
  • Data Science
  • Differential Equations
  • Engineering
  • Equations
  • Gaussian Processes
  • Information Science
  • Markov Processes
  • North Carolina
  • Probability
  • Random Variables
  • Real Numbers
  • Stationary Processes
  • Statistics
  • Stochastic Processes

Readers

  • Mathematical Modeling and Probability Theory.