Weak Convergence of Sums of Moving Averages in the Alpha-Stable Domain of Attraction.

Abstract

Skorohod has shown that the convergence of sums of i.i.d. random variables to an alpha-stable Levy process, with 0<alpha<2, holds in the weak J sub 1 sense. It is shown that for sums of moving averages with at least 2 non-zero coefficients, weak J sub 1 convergence cannot hold, however, if the moving average coefficients are positive, weak M sub 1 convergence usually does hold, Keywords: bisection method; sequences (mathematics).

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1987
Accession Number
ADA186430

Entities

People

  • Florin Avram

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Coefficients
  • Convergence
  • Inequalities
  • Mathematics
  • North Carolina
  • Oscillation
  • Probability
  • Probability Distributions
  • Random Variables
  • Scientific Research
  • Sequences
  • Statistics
  • Stochastic Processes
  • Topology
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.