Skip to main content

A General Compact Law of the Iterated Logarithm in Banach Spaces

  • Conference paper
  • 1314 Accesses

Part of the book series: Progress in Probability ((PRPR,volume 47))

Abstract

We study a general compact law of the iterated logarithm, the related cluster set, and also the cluster sets determined by random series in Banach spaces.

Research partially supported by an FWO Grant.

Research partially supported by NSF Grant 9703740.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • K. Alexander (1989a), Characterization of the cluster set of the LIL sequence in Banach space, Ann. Probab. 17, 737–759.

    Article  MathSciNet  MATH  Google Scholar 

  • K. Alexander (1989b), Unusual cluster sets for the LIL sequence in Banach space, Ann. Probab. 17, 1170–1185.

    Article  MathSciNet  MATH  Google Scholar 

  • M.M. Day (1973), Normed Linear Spaces, Third Edition, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • U. Einmahl (1993), Toward a general law of the iterated logarithm in Ba-nach space, Ann. Probab. 21, 2012–2045.

    Article  MathSciNet  MATH  Google Scholar 

  • U. Einmahl (1995), On the cluster set problem for the generalized law of the iterated logarithm in Euclidean space, Ann. Probab. 23, 817–851.

    Article  MathSciNet  MATH  Google Scholar 

  • U. Einmahl and J. Kuelbs (1999), Cluster sets for a generalized law of the iterated logarithm in Banach spaces. Preprint

    Google Scholar 

  • M. Klass, Toward a universal law of the iterated logarithm(I). Z. Wahrsch. Verw. Gebiete 36, 165–178.

    Google Scholar 

  • J. Kuelbs (1981), When is the cluster set of S n /a n empty? Ann. Probab. 9, 377–394.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Ledoux and M. Talagrand (1991), Probability in Banach Spaces, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • J. Lindenstrauss and L. Tzafriri (1977), Classical Banach Spaces I, Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  • I. Singer (1970), Bases in Banach Spaces I., Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media New York

About this paper

Cite this paper

Einmahl, U., Kuelbs, J. (2000). A General Compact Law of the Iterated Logarithm in Banach Spaces. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1358-1_17

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7111-6

  • Online ISBN: 978-1-4612-1358-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics