Advertisement

Weak Convergence of Moving Averages with Infinite Variance

  • Florin Avram
  • Murad S. Taqqu
Part of the Progress in Probability and Statistics book series (PRPR, volume 11)

Abstract

We survey results concerning the asymptotic behavior of moving averages that belong to the stable domain of attraction. Some of the methods are highlighted and new results announced.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Astrauskas, A. (1983). Limit theorems for sums of linearly generated random variables. Lithuanian Mat. Journal 23 (2), 127–134.MathSciNetGoogle Scholar
  2. [2]
    Avram, F. and Taqqu, M.S. (1984). Symmetric polynomials of random variables attracted to an infinitely divisible law. School of Operations Research and Industrial Engineering Technical Report No. 622, Cornell University, Ithaca. To appear in Z. Wahrscheinlichkeitstheorie verw. Geb.Google Scholar
  3. [3]
    Billingsley, P. (1968). Convergence of Probability Measures. Wiley: New York.zbMATHGoogle Scholar
  4. [4]
    Chatterji, S.D. (1969). An LP-convergence theorem. Ann. Math. Stat. 40, 1068–1070.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    Davis, R. and Resnick, S. (1985). Limit theory for moving averages with regularly varying tail probabilities. Ann. Prob. 13, 179–195.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    Feller, W. (1971). An Introduction to Probability Theory and Its Applications. Vol. II, 2nd Ed. Wiley: New York.zbMATHGoogle Scholar
  7. [7]
    Kawata, T. (1972). Fourier Analysis in Probability Theory. Academic Press: New York.zbMATHGoogle Scholar
  8. [8]
    Lamperti, J.W. (1962). Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104, 62–78.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    Maejima, M. (1983). On a class of self-similar processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 62, 235–245.CrossRefzbMATHMathSciNetGoogle Scholar
  10. [10]
    Maejima, M. (1983b). A self-similar process with nowhere bounded sample paths. Z. Wahrscheinlichkeitstheorie verw. Geb. 65, 115–119.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    Skorohod, A.V. (1957) Limit theorems for stochastic processes with independent increments. Theor. Probability Appl. 2, 138–171.CrossRefGoogle Scholar
  12. [12]
    Surgailis, D. (1983). Zones of attraction of self-similar multiple integrals. Lithuanian Mat. Journal 22, 327–430.CrossRefzbMATHGoogle Scholar
  13. [13]
    Taqqu, M.S. and Wolpert, R. (1983). Infinite variance self-similar processes subordinate to a Poisson measure. Z. Wahrscheinlichkeitstheorie verw. Geb. 62, 53–72.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Florin Avram
    • 1
  • Murad S. Taqqu
    • 2
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsBoston UniversityBostonUSA

Personalised recommendations