Skip to main content
SpringerLink
Log in

Conditional variance of symmetric stable variables

  • Chapter
Stable Processes and Related Topics

Part of the book series: Progress in Probabilty ((PRPR,volume 25))

Abstract

For two symmetric α-stable random variables with 1 < α < 2 we find a necessary and sufficient condition for the conditional variance to exist and be finite, we show it has a fixed functional form independent of their joint distribution, we describe its asymptotic behavior and we illustrate its global dependence on the joint distribution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Kanter “Linear sample spaces and stable processes”, J. Fund. Anal 9 (1972), 441–459.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Masry and S. Cambanis “Spectral density estimation for stationary stable processes”, Stochastic Proc. Appl. 18 (1984), 1–31.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Miller “Some results on symmetric stable distributions and processes”, Institute of Statistics Mimeo Series No. 1121 (1977), Univ. of North Carolina.

    Google Scholar 

  5. G. Samorodnitsky and M. Taqqu “Conditional moments of stable random variables”, preprint (1989).

    Google Scholar 

  6. S. Zabell “Continuous versions of regular conditional distributions”, Ann. Probab. 7 (1979), 159–165.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Wei Wu & Stamatis Cambanis

Authors
  1. Wei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stamatis Cambanis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Stamatis Cambanis

  2. Engineering Theory Center, Cornell University, Ithaca, NY, 14853, USA

    Gennady Samorodnitsky

  3. Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA, 02215, USA

    Murad S. Taqqu

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Birkhäuser Boston

About this chapter

Cite this chapter

Wu, W., Cambanis, S. (1991). Conditional variance of symmetric stable variables. In: Cambanis, S., Samorodnitsky, G., Taqqu, M.S. (eds) Stable Processes and Related Topics. Progress in Probabilty, vol 25. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6778-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-6778-9_4

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6780-2

  • Online ISBN: 978-1-4684-6778-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation