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
Stationary min-stable stochastic processes
Download PDF
Download PDF
  • Published: July 1986

Stationary min-stable stochastic processes

  • L. de Haan1 &
  • J. Pickands III2,3 

Probability Theory and Related Fields volume 72, pages 477–492 (1986)Cite this article

  • 235 Accesses

  • 62 Citations

  • Metrics details

Summary

We consider the class of stationary stochastic processes whose margins are jointly min-stable. We show how the scalar elements can be generated by a single realization of a standard homogeneous Poisson process on the upper half-strip [0,1]×R + and a group of L 1-isometries. We include a Dobrushin-like result for the realizations in continuous time.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • Cramér, H., Leadbetter, M.R.: Stationary and related stochastic processes. New York: J. Wiley 1967

    Google Scholar 

  • Deheuvels, P.: Point processes and multivariate extreme values. J. Multivariate Anal. 13, 257–272 (1983)

    Google Scholar 

  • Dobrushin, R.L.: Properties of sample functions of a stationary gaussian process. Teor. Veroyatn. Primen. 5, 132–134 (1960)

    Google Scholar 

  • Galambos, J.: The asymptotic theory of extreme order statistics. New York: Wiley, 1978

    Google Scholar 

  • Haan, L. de, Resnick, S.I.: Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 40, 317–337 (1977)

    Google Scholar 

  • Haan, L. de: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984)

    Google Scholar 

  • Halmos, P.R.: Measure theory. Princeton: D. van Nostrand 1950

    Google Scholar 

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

    Google Scholar 

  • Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and related properties of random sequences and processes. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • Parry, W., Tuncel, S.: Classification problems in ergodic theory. Cambridge: University Press 1982

    Google Scholar 

  • Pickands, J. III: The two-dimensional Poisson process and extremal processes. J. Appl. Probab. 8, 745–756 (1971)

    Google Scholar 

  • Royden, H.L.: Real analysis. 2nd ed. New York: Macmillan 1968

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Erasmus University Rotterdam, pb 1738, 3000 DR, Rotterdam, The Netherlands

    L. de Haan

  2. Erasmus University, Rotterdam, The Netherlands

    J. Pickands III

  3. University of Pennsylvania, Philadelphia, USA

    J. Pickands III

Authors
  1. L. de Haan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Pickands III
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

de Haan, L., Pickands, J. Stationary min-stable stochastic processes. Probab. Th. Rel. Fields 72, 477–492 (1986). https://doi.org/10.1007/BF00344716

Download citation

  • Received: 14 November 1983

  • Revised: 22 January 1986

  • Issue Date: July 1986

  • DOI: https://doi.org/10.1007/BF00344716

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

Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Poisson Process
  • Continuous Time
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