Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Stable mixed moving averages
Download PDF
Download PDF
  • Published: December 1993

Stable mixed moving averages

  • Donatas Surgailis1 nAff2,
  • Jan Rosinski1 nAff3,
  • V. Mandrekar1 nAff4 &
  • …
  • Stamatis Cambanis1 

Probability Theory and Related Fields volume 97, pages 543–558 (1993)Cite this article

  • 248 Accesses

  • 44 Citations

  • Metrics details

Summary

The class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter function and the mixing measure, leading to a generalization of a theorem of Kanter (1973) for usual moving averages. Stable mixed moving averages contain sums of independent stable moving averages, are ergodic and are not harmonizable. Also a class of stable mixed moving averages is constructed with the reflection positivity property.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Adler, R.J., Cambanis, S., Samorodnitsky, G.: On stable Markov processes. Stochastic Proc. Appl.34, 1–17 (1990)

    Google Scholar 

  2. Cambanis, S., Hardin, C.D., Jr., Weron, A.: Ergodic properties of stationary stable processes. Stochastic Proc. Appl.24, 1–18 (1987)

    Google Scholar 

  3. Dunford, N., Schwartz, J.T.: Linear operators part I: General theory. New York: Wiley 1988

    Google Scholar 

  4. Hardin, C.D., Jr.: On the spectral representation of symmetric stable processes. J. Multivariate Anal.12, 385–401 (1982)

    Google Scholar 

  5. Kanter, M.: TheL p norm of sums of translates of a function. Trans. Am. Math. Soc.179, 35–47 (1973)

    Google Scholar 

  6. Klein, A.: GaussianOS-positive processes. Z. Wahrscheinlichkeitstheor Verw. Geb.40, 115–124 (1977)

    Google Scholar 

  7. Klein, A.: A generalization of Markov processes. Ann. Probab.6, 128–132 (1978)

    Google Scholar 

  8. Makagon, A., Mandrekar, V.: The spectral representation of stable processes: Harmonizability and regularity. Probab Theory Relat. Fields85, 1–11 (1990)

    Google Scholar 

  9. Meyer, P.A.: Note sur les processus d'Ornstein-Uhlenbeck. In: Azéma, J., Yo., M. (eds.) Sémin. Probab. XVI (Lect. Notes Math., vol. 920, pp. 95–133) Berlin Heidelberg New York: Springer 1982

    Google Scholar 

  10. Parthasarathy, K.R., Schmidt, K.: Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. (Lect. Notes Math., vol. 272) Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  11. Surgailis, D.: On Poisson multiple stochastic integrals and associated equilibrium Markov processes. In. Kallianpur, G. (ed.) Theory and application of random fields. (Lect. Notes Control Inf. Sci., vol. 49, pp. 233–248) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

Download references

Author information

Author notes
  1. Donatas Surgailis

    Present address: Institute of Mathematics and Informatics, Lithuanian Academy of Sciences, 2600, Vilnius, Lithuania

  2. Jan Rosinski

    Present address: Department of Mathematics, University of Tennessee, 37996, Knoxville, TN, USA

  3. V. Mandrekar

    Present address: Department of Statistics and Probability, Michigan State University, 48824, East Lansing, MI, USA

Authors and Affiliations

  1. Center for Stochastic Processes, Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA

    Donatas Surgailis, Jan Rosinski, V. Mandrekar & Stamatis Cambanis

Authors
  1. Donatas Surgailis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Rosinski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Mandrekar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stamatis Cambanis
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by AFSOR Contract 91-0030

Research also supported by ARO DAAL-91-G-0176

Research also supported by AFOSR 90-0168

Research also supported by ONR N00014-91-J-0277

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Surgailis, D., Rosinski, J., Mandrekar, V. et al. Stable mixed moving averages. Probab. Th. Rel. Fields 97, 543–558 (1993). https://doi.org/10.1007/BF01192963

Download citation

  • Received: 05 May 1992

  • Revised: 21 May 1993

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01192963

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Mathematics Subject Classification (1991)

  • 60G10
  • 60B05
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature